Question

1. what are the x-intercept and y-intercept of each line? use the intercepts to sketch a graph of each line. a) $5x - 2y - 20 = 0$ b) $y = 4$ c) $x = 2$

Explanation:

Part (a)

Step1: Find x - intercept (set y = 0)

Set \( y = 0 \) in \( 5x - 2y - 20 = 0 \). Then \( 5x-2(0)-20 = 0 \), which simplifies to \( 5x=20 \). Solving for \( x \), we get \( x=\frac{20}{5}=4 \). So the x - intercept is \( (4,0) \).

Step2: Find y - intercept (set x = 0)

Set \( x = 0 \) in \( 5x - 2y - 20 = 0 \). Then \( 5(0)-2y - 20 = 0 \), which simplifies to \( - 2y=20 \). Solving for \( y \), we get \( y=-10 \). So the y - intercept is \( (0, - 10) \).

Step1: Analyze the line \( y = 4 \)

The line \( y = 4 \) is a horizontal line. For a horizontal line \( y = k \) (where \( k = 4 \) here), the y - intercept is the point where \( x = 0 \). Since \( y=4 \) for all \( x \), when \( x = 0 \), \( y = 4 \), so the y - intercept is \( (0,4) \).

Step2: Check for x - intercept

A horizontal line \( y = 4 \) (where \( y
eq0 \)) never intersects the x - axis (because the x - axis is \( y = 0 \)), so there is no x - intercept.

Step1: Analyze the line \( x = 2 \)

The line \( x = 2 \) is a vertical line. For a vertical line \( x = k \) (where \( k = 2 \) here), the x - intercept is the point where \( y = 0 \). Since \( x = 2 \) for all \( y \), when \( y = 0 \), \( x = 2 \), so the x - intercept is \( (2,0) \).

Step2: Check for y - intercept

A vertical line \( x = 2 \) (where \( x
eq0 \)) never intersects the y - axis (because the y - axis is \( x = 0 \)), so there is no y - intercept.

Answer:

(a):
x - intercept: \( (4,0) \), y - intercept: \( (0, - 10) \)

Part (b)