Question

y = \frac{1}{3}x - 10

Explanation:

This is a linear equation in the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. If we want to find the x - intercept, we set \( y = 0 \) and solve for \( x \); if we want to find the y - intercept, we set \( x = 0 \) and solve for \( y \). Let's assume we want to find the x - intercept.

Step 1: Set \( y = 0 \)

We substitute \( y = 0 \) into the equation \( y=\frac{1}{3}x - 10 \), so we get \( 0=\frac{1}{3}x-10 \).

Step 2: Solve for \( x \)

First, we add 10 to both sides of the equation: \( 0 + 10=\frac{1}{3}x-10 + 10 \), which simplifies to \( 10=\frac{1}{3}x \). Then we multiply both sides by 3 to isolate \( x \): \( x=10\times3 = 30 \).

If we want to find the y - intercept:

Step 1: Set \( x = 0 \)

Substitute \( x = 0 \) into the equation \( y=\frac{1}{3}x-10 \), we have \( y=\frac{1}{3}(0)-10 \).

Step 2: Calculate \( y \)

\( y = 0 - 10=- 10 \).

(The answer depends on what is being asked about the equation. If it's the x - intercept, the answer is 30; if it's the y - intercept, the answer is - 10; if it's about the slope, the slope \( m=\frac{1}{3}\))

For example, if the question is "Find the x - intercept of the line \( y = \frac{1}{3}x-10 \)":

Answer:

30

If the question is "Find the y - intercept of the line \( y=\frac{1}{3}x - 10 \)":