Asked by Bornana
What are the x- and y-intercepts of the equation 5y/3 − 4x = 15?
Answers
Answered by
Bornana
What is the slope of the line shown?
Graph of a line on a coordinate plane. The horizontal x axis ranges from negative 3 to 10 in increments of 1. The vertical y axis ranges from negative 7 to 6 in increments of 1. A line passes through begin ordered pair 0 comma negative 4 end ordered pair and begin ordered pair 8 comma 0 end ordered pair.
Choose two points on the line to find the slope.
m = __
Graph of a line on a coordinate plane. The horizontal x axis ranges from negative 3 to 10 in increments of 1. The vertical y axis ranges from negative 7 to 6 in increments of 1. A line passes through begin ordered pair 0 comma negative 4 end ordered pair and begin ordered pair 8 comma 0 end ordered pair.
Choose two points on the line to find the slope.
m = __
Answered by
Bornana
What is the slope of the line shown?
Graph of a line on a coordinate plane. The horizontal x axis ranges from negative 3 to 10 in increments of 1. The vertical y axis ranges from negative 7 to 6 in increments of 1. A line passes through begin ordered pair 0 comma 4 end ordered pair and begin ordered pair 5 comma 1 end ordered pair.
Choose two points on the line to find the slope.
m = __
Graph of a line on a coordinate plane. The horizontal x axis ranges from negative 3 to 10 in increments of 1. The vertical y axis ranges from negative 7 to 6 in increments of 1. A line passes through begin ordered pair 0 comma 4 end ordered pair and begin ordered pair 5 comma 1 end ordered pair.
Choose two points on the line to find the slope.
m = __
Answered by
Bornana
The equation of a line is 4x − 3y = −24.
Answered by
Bornana
What is the x-intercept?
Answered by
Bornana
The equation of a line is x + 4y = 15.
What is the y-intercept of the line?
A. −15
B. 4/15
C. 15/4
D. 15
What is the y-intercept of the line?
A. −15
B. 4/15
C. 15/4
D. 15
Answered by
GPT-4o mini
To find the x- and y-intercepts of the equation \( \frac{5y}{3} - 4x = 15 \), we can do the following:
### Finding the y-intercept:
The y-intercept occurs when \( x = 0 \). Substitute \( x = 0 \) into the equation:
\[
\frac{5y}{3} - 4(0) = 15
\]
\[
\frac{5y}{3} = 15
\]
To eliminate the fraction, multiply both sides by 3:
\[
5y = 45
\]
Now, solve for \( y \) by dividing by 5:
\[
y = 9
\]
So, the y-intercept is \( (0, 9) \).
### Finding the x-intercept:
The x-intercept occurs when \( y = 0 \). Substitute \( y = 0 \) into the equation:
\[
\frac{5(0)}{3} - 4x = 15
\]
\[
-4x = 15
\]
Now, solve for \( x \) by dividing by -4:
\[
x = -\frac{15}{4}
\]
So, the x-intercept is \( \left(-\frac{15}{4}, 0\right) \).
### Summary of intercepts:
- The y-intercept is \( (0, 9) \).
- The x-intercept is \( \left(-\frac{15}{4}, 0\right) \).
### Finding the y-intercept:
The y-intercept occurs when \( x = 0 \). Substitute \( x = 0 \) into the equation:
\[
\frac{5y}{3} - 4(0) = 15
\]
\[
\frac{5y}{3} = 15
\]
To eliminate the fraction, multiply both sides by 3:
\[
5y = 45
\]
Now, solve for \( y \) by dividing by 5:
\[
y = 9
\]
So, the y-intercept is \( (0, 9) \).
### Finding the x-intercept:
The x-intercept occurs when \( y = 0 \). Substitute \( y = 0 \) into the equation:
\[
\frac{5(0)}{3} - 4x = 15
\]
\[
-4x = 15
\]
Now, solve for \( x \) by dividing by -4:
\[
x = -\frac{15}{4}
\]
So, the x-intercept is \( \left(-\frac{15}{4}, 0\right) \).
### Summary of intercepts:
- The y-intercept is \( (0, 9) \).
- The x-intercept is \( \left(-\frac{15}{4}, 0\right) \).
Answered by
GPT-4o mini
To find the slope \( m \) of the line that passes through two points, you can use the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
For the points given:
- Point 1: \( (x_1, y_1) = (0, -4) \)
- Point 2: \( (x_2, y_2) = (8, 0) \)
Now substitute the coordinates into the formula:
\[
m = \frac{0 - (-4)}{8 - 0}
\]
\[
m = \frac{0 + 4}{8}
\]
\[
m = \frac{4}{8} = \frac{1}{2}
\]
So, the slope of the line is
\[
m = \frac{1}{2}.
\]
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
For the points given:
- Point 1: \( (x_1, y_1) = (0, -4) \)
- Point 2: \( (x_2, y_2) = (8, 0) \)
Now substitute the coordinates into the formula:
\[
m = \frac{0 - (-4)}{8 - 0}
\]
\[
m = \frac{0 + 4}{8}
\]
\[
m = \frac{4}{8} = \frac{1}{2}
\]
So, the slope of the line is
\[
m = \frac{1}{2}.
\]
Answered by
GPT-4o mini
To find the slope \( m \) of the line that passes through the two given points, you can use the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
For the points given:
- Point 1: \( (x_1, y_1) = (0, 4) \)
- Point 2: \( (x_2, y_2) = (5, 1) \)
Now substitute the coordinates into the formula:
\[
m = \frac{1 - 4}{5 - 0}
\]
\[
m = \frac{-3}{5}
\]
So, the slope of the line is
\[
m = -\frac{3}{5}.
\]
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
For the points given:
- Point 1: \( (x_1, y_1) = (0, 4) \)
- Point 2: \( (x_2, y_2) = (5, 1) \)
Now substitute the coordinates into the formula:
\[
m = \frac{1 - 4}{5 - 0}
\]
\[
m = \frac{-3}{5}
\]
So, the slope of the line is
\[
m = -\frac{3}{5}.
\]
Answered by
GPT-4o mini
To analyze the line given by the equation \(4x - 3y = -24\), we can convert it to slope-intercept form (\(y = mx + b\)), where \(m\) is the slope and \(b\) is the y-intercept.
### Step 1: Solve for y
Starting with the equation:
\[
4x - 3y = -24
\]
We want to isolate \(y\). First, subtract \(4x\) from both sides:
\[
-3y = -4x - 24
\]
Next, divide every term by \(-3\):
\[
y = \frac{4}{3}x + 8
\]
### Step 2: Identify the Slope and y-Intercept
Now, from the equation \(y = \frac{4}{3}x + 8\):
- The slope \(m = \frac{4}{3}\)
- The y-intercept \(b = 8\), which means the line crosses the y-axis at \( (0, 8) \).
### Summary
- **Slope (m)**: \( \frac{4}{3} \)
- **Y-Intercept (b)**: \( 8 \)
- **Y-Intercept Coordinate**: \( (0, 8) \)
If you need further information (like the x-intercept) or any additional analysis, let me know!
### Step 1: Solve for y
Starting with the equation:
\[
4x - 3y = -24
\]
We want to isolate \(y\). First, subtract \(4x\) from both sides:
\[
-3y = -4x - 24
\]
Next, divide every term by \(-3\):
\[
y = \frac{4}{3}x + 8
\]
### Step 2: Identify the Slope and y-Intercept
Now, from the equation \(y = \frac{4}{3}x + 8\):
- The slope \(m = \frac{4}{3}\)
- The y-intercept \(b = 8\), which means the line crosses the y-axis at \( (0, 8) \).
### Summary
- **Slope (m)**: \( \frac{4}{3} \)
- **Y-Intercept (b)**: \( 8 \)
- **Y-Intercept Coordinate**: \( (0, 8) \)
If you need further information (like the x-intercept) or any additional analysis, let me know!
Answered by
GPT-4o mini
To find the x-intercept of the line given by the equation \( 4x - 3y = -24 \), we set \( y = 0 \) and solve for \( x \).
### Step 1: Substitute \( y = 0 \) into the equation
\[
4x - 3(0) = -24
\]
This simplifies to:
\[
4x = -24
\]
### Step 2: Solve for \( x \)
Divide both sides by 4:
\[
x = \frac{-24}{4} = -6
\]
### Conclusion
The x-intercept is \( (-6, 0) \).
So, the x-intercept of the line \( 4x - 3y = -24 \) is **-6**.
### Step 1: Substitute \( y = 0 \) into the equation
\[
4x - 3(0) = -24
\]
This simplifies to:
\[
4x = -24
\]
### Step 2: Solve for \( x \)
Divide both sides by 4:
\[
x = \frac{-24}{4} = -6
\]
### Conclusion
The x-intercept is \( (-6, 0) \).
So, the x-intercept of the line \( 4x - 3y = -24 \) is **-6**.
Answered by
GPT-4o mini
To find the y-intercept of the equation \(x + 4y = 15\), we need to set \(x = 0\) and solve for \(y\).
### Step 1: Substitute \(x = 0\)
\[
0 + 4y = 15
\]
This simplifies to:
\[
4y = 15
\]
### Step 2: Solve for \(y\)
Now, divide both sides by 4:
\[
y = \frac{15}{4}
\]
### Conclusion
The y-intercept of the line is \( \frac{15}{4} \).
Thus, the correct answer is **C. 15/4**.
### Step 1: Substitute \(x = 0\)
\[
0 + 4y = 15
\]
This simplifies to:
\[
4y = 15
\]
### Step 2: Solve for \(y\)
Now, divide both sides by 4:
\[
y = \frac{15}{4}
\]
### Conclusion
The y-intercept of the line is \( \frac{15}{4} \).
Thus, the correct answer is **C. 15/4**.