Question
2x + 3y = –6
–4x + 3y = 12
x – y = 5 dont just choose these 3 there might be more than 3? less? or one of the answers not right?
Which equations are in standard form? Check all that apply
y = 2x + 5
2x + 3y = –6
–4x + 3y = 12
y = y equals StartFraction 3 Over 2 EndFraction x minus 9.x – 9
StartFraction one-half EndFraction x plus 3 equals 6.x + 3 = 6
x – y = 5
5x + 3y = 5 x plus 3 y equals StartFraction one-half EndFraction.
–4x + 3y = 12
x – y = 5 dont just choose these 3 there might be more than 3? less? or one of the answers not right?
Which equations are in standard form? Check all that apply
y = 2x + 5
2x + 3y = –6
–4x + 3y = 12
y = y equals StartFraction 3 Over 2 EndFraction x minus 9.x – 9
StartFraction one-half EndFraction x plus 3 equals 6.x + 3 = 6
x – y = 5
5x + 3y = 5 x plus 3 y equals StartFraction one-half EndFraction.
Answers
Answer
only 2
2x + 3y = –6
x – y = 5
The drama club sold $779 worth of tickets to the school play. Student tickets cost $3 apiece and tickets for everyone else cost $5 each. What equation relates the number of student tickets that were sold, s, and the number of other tickets that were sold, t, written in standard form?
s +
t =
2x + 3y = –6
x – y = 5
The drama club sold $779 worth of tickets to the school play. Student tickets cost $3 apiece and tickets for everyone else cost $5 each. What equation relates the number of student tickets that were sold, s, and the number of other tickets that were sold, t, written in standard form?
s +
t =
Answer
Which is the graph of 4x – 3y = 12? A coordinate plane with a line passing through (0, negative 3) and (1, 1).A coordinate plane with a line passing through (negative 2, negative 1) and (4, 1).A coordinate plane with a line passing through (0, negative 12) and (3, 0).A coordinate plane with a line passing through (0, negative 4) and (3, 0).
Answer
choose the fourth graph or i can also say choose the line thats under -4 but the less steeper one
The standard form of a linear equation is Ax + By = C. If B = 0 and A and C are positive, which best describes the graph of this equation?
The graph is a vertical line.
The graph is a horizontal line.
The graph is a line with a positive slope.
The graph is a line with a negative slope.
The standard form of a linear equation is Ax + By = C. If B = 0 and A and C are positive, which best describes the graph of this equation?
The graph is a vertical line.
The graph is a horizontal line.
The graph is a line with a positive slope.
The graph is a line with a negative slope.
Answer
graph 2x-5y=10
Answer
whats x and y intercept
Answered by
GPT-4o mini
To determine which equations are in standard form, we need to look for equations that are typically written in the general format \( Ax + By = C \), where \( A \), \( B \), and \( C \) are integers, \( A \) is non-negative, and \( A \), \( B \), and \( C \) should usually not have any fractions.
Let's evaluate each of the equations you've listed:
1. **y = 2x + 5**
- This is in slope-intercept form, not standard form.
2. **2x + 3y = –6**
- This is in standard form (A = 2, B = 3, C = -6).
3. **–4x + 3y = 12**
- This is also in standard form (A = -4, B = 3, C = 12). However, typically A should be non-negative. It's still a form of standard, though conventionally might need A to be positive.
4. **y = (3/2)x - 9**
- This is also in slope-intercept form, not standard form.
5. **1/2 x + 3 = 6**
- To put this into standard form, you'd need to rearrange it: \( \frac{1}{2}x = 3 \) or \( x = 6 \). This doesn't fit standard form either since it contains a fraction.
6. **x – y = 5**
- This is in standard form (A = 1, B = -1, C = 5).
7. **5x + 3y = 5**
- This is also in standard form (A = 5, B = 3, C = 5).
8. **x + 3y = 1/2**
- This has a fraction on the right side. It's not in standard form according to the typical definition.
### Summary of Equations in Standard Form:
- **2x + 3y = –6**
- **–4x + 3y = 12**
- **x – y = 5**
- **5x + 3y = 5**
Hence, the equations that are in standard form are:
- **2x + 3y = –6**
- **–4x + 3y = 12**
- **x – y = 5**
- **5x + 3y = 5**
Let's evaluate each of the equations you've listed:
1. **y = 2x + 5**
- This is in slope-intercept form, not standard form.
2. **2x + 3y = –6**
- This is in standard form (A = 2, B = 3, C = -6).
3. **–4x + 3y = 12**
- This is also in standard form (A = -4, B = 3, C = 12). However, typically A should be non-negative. It's still a form of standard, though conventionally might need A to be positive.
4. **y = (3/2)x - 9**
- This is also in slope-intercept form, not standard form.
5. **1/2 x + 3 = 6**
- To put this into standard form, you'd need to rearrange it: \( \frac{1}{2}x = 3 \) or \( x = 6 \). This doesn't fit standard form either since it contains a fraction.
6. **x – y = 5**
- This is in standard form (A = 1, B = -1, C = 5).
7. **5x + 3y = 5**
- This is also in standard form (A = 5, B = 3, C = 5).
8. **x + 3y = 1/2**
- This has a fraction on the right side. It's not in standard form according to the typical definition.
### Summary of Equations in Standard Form:
- **2x + 3y = –6**
- **–4x + 3y = 12**
- **x – y = 5**
- **5x + 3y = 5**
Hence, the equations that are in standard form are:
- **2x + 3y = –6**
- **–4x + 3y = 12**
- **x – y = 5**
- **5x + 3y = 5**
Answered by
GPT-4o mini
To create an equation that relates the number of student tickets sold, \( s \), and the number of other tickets sold, \( t \), we first need to account for the total revenue from ticket sales.
Given:
- Student tickets cost $3 each.
- Other tickets cost $5 each.
- The total revenue from ticket sales is $779.
The equation for the total revenue can be set up as follows:
\[
3s + 5t = 779
\]
To write this in standard form \( Ax + By = C \), we identify:
- \( A = 3 \)
- \( B = 5 \)
- \( C = 779 \)
So the equation is already in standard form:
\[
3s + 5t = 779
\]
Thus, the equation relating the number of student tickets that were sold, \( s \), and the number of other tickets that were sold, \( t \), is:
\[
3s + 5t = 779
\]
Given:
- Student tickets cost $3 each.
- Other tickets cost $5 each.
- The total revenue from ticket sales is $779.
The equation for the total revenue can be set up as follows:
\[
3s + 5t = 779
\]
To write this in standard form \( Ax + By = C \), we identify:
- \( A = 3 \)
- \( B = 5 \)
- \( C = 779 \)
So the equation is already in standard form:
\[
3s + 5t = 779
\]
Thus, the equation relating the number of student tickets that were sold, \( s \), and the number of other tickets that were sold, \( t \), is:
\[
3s + 5t = 779
\]
Answered by
GPT-4o mini
To determine the graph of the equation \(4x - 3y = 12\), let's first convert this equation into slope-intercept form (\(y = mx + b\)) to identify its y-intercept and slope.
1. Start with the equation:
\[
4x - 3y = 12
\]
2. Rearrange to solve for \(y\):
\[
-3y = -4x + 12
\]
\[
y = \frac{4}{3}x - 4
\]
From this, we can see:
- The **y-intercept** is \(-4\) (when \(x = 0\)).
- The **slope** is \(\frac{4}{3}\), which means for every 3 units we go to the right in \(x\), we move 4 units up in \(y\).
Now we can determine which of the given graphs is correct based on the y-intercept and any other points that lie on the line.
### Testing the options:
1. **A line passing through (0, -3) and (1, 1):**
- It goes through \(y = -3\) when \(x = 0\), which does not match our line.
2. **A line passing through (-2, -1) and (4, 1):**
- These points don't align with our y-intercept of -4.
3. **A line passing through (0, -12) and (3, 0):**
- It has a y-intercept of \(-12\), which does not match.
4. **A line passing through (0, -4) and (3, 0):**
- It passes through \(y = -4\) when \(x = 0\), which matches our y-intercept.
- To check the point (3, 0):
\[
4(3) - 3(0) = 12 \quad \text{(this point also satisfies the equation)}.
\]
### Conclusion:
The graph that represents the equation \(4x - 3y = 12\) is:
**A coordinate plane with a line passing through (0, -4) and (3, 0).**
1. Start with the equation:
\[
4x - 3y = 12
\]
2. Rearrange to solve for \(y\):
\[
-3y = -4x + 12
\]
\[
y = \frac{4}{3}x - 4
\]
From this, we can see:
- The **y-intercept** is \(-4\) (when \(x = 0\)).
- The **slope** is \(\frac{4}{3}\), which means for every 3 units we go to the right in \(x\), we move 4 units up in \(y\).
Now we can determine which of the given graphs is correct based on the y-intercept and any other points that lie on the line.
### Testing the options:
1. **A line passing through (0, -3) and (1, 1):**
- It goes through \(y = -3\) when \(x = 0\), which does not match our line.
2. **A line passing through (-2, -1) and (4, 1):**
- These points don't align with our y-intercept of -4.
3. **A line passing through (0, -12) and (3, 0):**
- It has a y-intercept of \(-12\), which does not match.
4. **A line passing through (0, -4) and (3, 0):**
- It passes through \(y = -4\) when \(x = 0\), which matches our y-intercept.
- To check the point (3, 0):
\[
4(3) - 3(0) = 12 \quad \text{(this point also satisfies the equation)}.
\]
### Conclusion:
The graph that represents the equation \(4x - 3y = 12\) is:
**A coordinate plane with a line passing through (0, -4) and (3, 0).**
Answered by
GPT-4o mini
In the standard form of a linear equation, \(Ax + By = C\):
- If \(B = 0\), the equation reduces to \(Ax = C\).
Since \(A\) and \(C\) are positive, the equation can be rewritten as:
\[
x = \frac{C}{A}
\]
This equation indicates that \(x\) is equal to a constant value, \(\frac{C}{A}\), regardless of the value of \(y\).
### Graph Characteristics:
- Since \(x\) is constant, the graph represents all points where \(x\) is equal to that constant value.
- The graph is a **vertical line**.
### Conclusion:
The correct description of the graph in this case is:
**The graph is a vertical line.**
- If \(B = 0\), the equation reduces to \(Ax = C\).
Since \(A\) and \(C\) are positive, the equation can be rewritten as:
\[
x = \frac{C}{A}
\]
This equation indicates that \(x\) is equal to a constant value, \(\frac{C}{A}\), regardless of the value of \(y\).
### Graph Characteristics:
- Since \(x\) is constant, the graph represents all points where \(x\) is equal to that constant value.
- The graph is a **vertical line**.
### Conclusion:
The correct description of the graph in this case is:
**The graph is a vertical line.**
Answered by
GPT-4o mini
To graph the equation \(2x - 5y = 10\), we'll first rewrite it in slope-intercept form (\(y = mx + b\)), which makes it easier to identify the slope and the y-intercept.
### Step 1: Rearranging to Slope-Intercept Form
Start with the equation:
\[
2x - 5y = 10
\]
Now, solve for \(y\):
\[
-5y = -2x + 10
\]
Divide both sides by \(-5\):
\[
y = \frac{2}{5}x - 2
\]
### Step 2: Identify the Slope and Y-Intercept
From the equation \(y = \frac{2}{5}x - 2\):
- The **slope** (\(m\)) is \(\frac{2}{5}\).
- The **y-intercept** (\(b\)) is \(-2\), meaning the line crosses the y-axis at \((0, -2)\).
### Step 3: Find Another Point Using the Slope
Having \(m = \frac{2}{5}\) means for every 5 units you move to the right (positive x-direction), you move up 2 units (positive y-direction).
Starting from the y-intercept:
1. From \((0, -2)\):
- Move 5 units to the right to \(x = 5\).
- Move 2 units up to \(y = 0\).
- This gives the point \((5, 0)\).
### Step 4: Plotting the Points
Now that we have two points:
- **Point 1**: (0, -2)
- **Point 2**: (5, 0)
### Step 5: Draw the Line
1. Plot the points (0, -2) and (5, 0) on a coordinate plane.
2. Draw a straight line through these points, extending it in both directions.
### Summary
The line representing the equation \(2x - 5y = 10\) will pass through the point (0, -2) and (5, 0) with a slope of \(\frac{2}{5}\).
If you need a visual representation, you could use graphing tools or graphing paper to plot the points and draw the line accordingly.
### Step 1: Rearranging to Slope-Intercept Form
Start with the equation:
\[
2x - 5y = 10
\]
Now, solve for \(y\):
\[
-5y = -2x + 10
\]
Divide both sides by \(-5\):
\[
y = \frac{2}{5}x - 2
\]
### Step 2: Identify the Slope and Y-Intercept
From the equation \(y = \frac{2}{5}x - 2\):
- The **slope** (\(m\)) is \(\frac{2}{5}\).
- The **y-intercept** (\(b\)) is \(-2\), meaning the line crosses the y-axis at \((0, -2)\).
### Step 3: Find Another Point Using the Slope
Having \(m = \frac{2}{5}\) means for every 5 units you move to the right (positive x-direction), you move up 2 units (positive y-direction).
Starting from the y-intercept:
1. From \((0, -2)\):
- Move 5 units to the right to \(x = 5\).
- Move 2 units up to \(y = 0\).
- This gives the point \((5, 0)\).
### Step 4: Plotting the Points
Now that we have two points:
- **Point 1**: (0, -2)
- **Point 2**: (5, 0)
### Step 5: Draw the Line
1. Plot the points (0, -2) and (5, 0) on a coordinate plane.
2. Draw a straight line through these points, extending it in both directions.
### Summary
The line representing the equation \(2x - 5y = 10\) will pass through the point (0, -2) and (5, 0) with a slope of \(\frac{2}{5}\).
If you need a visual representation, you could use graphing tools or graphing paper to plot the points and draw the line accordingly.
Answered by
GPT-4o mini
To find the x-intercept and y-intercept of the equation \(2x - 5y = 10\), we can follow these steps:
### 1. Finding the Y-Intercept
The y-intercept occurs when \(x = 0\). Substitute \(x = 0\) into the equation:
\[
2(0) - 5y = 10
\]
\[
-5y = 10
\]
\[
y = -2
\]
So, the **y-intercept** is at the point \((0, -2)\).
### 2. Finding the X-Intercept
The x-intercept occurs when \(y = 0\). Substitute \(y = 0\) into the equation:
\[
2x - 5(0) = 10
\]
\[
2x = 10
\]
\[
x = 5
\]
So, the **x-intercept** is at the point \((5, 0)\).
### Summary
- **Y-Intercept**: \((0, -2)\)
- **X-Intercept**: \((5, 0)\)
These points correspond to where the line crosses the y-axis and x-axis, respectively.
### 1. Finding the Y-Intercept
The y-intercept occurs when \(x = 0\). Substitute \(x = 0\) into the equation:
\[
2(0) - 5y = 10
\]
\[
-5y = 10
\]
\[
y = -2
\]
So, the **y-intercept** is at the point \((0, -2)\).
### 2. Finding the X-Intercept
The x-intercept occurs when \(y = 0\). Substitute \(y = 0\) into the equation:
\[
2x - 5(0) = 10
\]
\[
2x = 10
\]
\[
x = 5
\]
So, the **x-intercept** is at the point \((5, 0)\).
### Summary
- **Y-Intercept**: \((0, -2)\)
- **X-Intercept**: \((5, 0)\)
These points correspond to where the line crosses the y-axis and x-axis, respectively.
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