Question

1. find the y-intercept of the line represented by the equation below. y - 5x = -3

Explanation:

Step1: Recall y-intercept definition

The y - intercept of a line is the value of \( y \) when \( x = 0 \). Also, the slope - intercept form of a line is \( y=mx + b \), where \( b \) is the y - intercept. We can rewrite the given equation in slope - intercept form.
Given equation: \( y-5x=-3 \)

Step2: Solve for y

Add \( 5x \) to both sides of the equation:
\( y-5x + 5x=-3 + 5x \)
Simplify to get \( y = 5x-3 \)

Step3: Identify the y - intercept

In the slope - intercept form \( y=mx + b \), comparing \( y = 5x-3 \) with \( y=mx + b \), we can see that when \( x = 0 \), \( y=-3 \). Also, the value of \( b\) (the y - intercept) is - 3. We can also directly substitute \( x = 0 \) into the original equation:
Substitute \( x = 0 \) into \( y-5x=-3 \)
\( y-5(0)=-3 \)
\( y-0=-3 \)
\( y=-3 \)

Answer:

The y - intercept is \(-3\)