2x + 3y = –6

Question

–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.

Answer 1

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

Answer 2

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 =

Answer 3

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:

\[ 3s + 5t = 779 \]

Answer 4

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 5

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).

Answer 6

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.

Answer 7

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.

Answer 8

graph 2x-5y=10

Answer 9

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.

Answer 10

whats x and y intercept

Answer 11

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.