Question

5.38. on graph paper, plot the points (-3, 7) and (2, -3) and draw a line through them. then name the x- and y-intercepts of the line.

Explanation:

Step1: Find the slope of the line

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). For points \((-3, 7)\) and \((2, -3)\), we have \( x_1=-3,y_1 = 7,x_2=2,y_2=-3 \). So \( m=\frac{-3 - 7}{2-(-3)}=\frac{-10}{5}=-2 \).

Step2: Find the equation of the line

Using the point - slope form \( y - y_1=m(x - x_1) \), we can use the point \((-3,7)\). So \( y - 7=-2(x+3) \). Expand it: \( y-7=-2x - 6 \), then \( y=-2x+1 \).

Step3: Find the x - intercept

The x - intercept is the value of \( x \) when \( y = 0 \). Set \( y = 0 \) in \( y=-2x + 1 \), we get \( 0=-2x+1 \). Solve for \( x \): \( 2x = 1 \), so \( x=\frac{1}{2}=0.5 \).

Step4: Find the y - intercept

The y - intercept is the value of \( y \) when \( x = 0 \). Set \( x = 0 \) in \( y=-2x + 1 \), we get \( y=1 \).

Answer:

The x - intercept is \( \frac{1}{2} \) (or \( 0.5 \)) and the y - intercept is \( 1 \).