What are the x- and y-intercepts of the equation 5y/3 − 4x = 15?

Answer 1

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 \( \left(-\frac{15}{4}, 0\right) \).

Answer 2

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 = __

Answer 3

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

\[ m = \frac{1}{2}. \]

Answer 4

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 = __

Answer 5

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

\[ m = -\frac{3}{5}. \]

Answer 6

The equation of a line is 4x − 3y = −24.

Answer 7

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!

Answer 8

What is the x-intercept?

Answer 9

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.

Answer 10

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

Answer 11

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.