Question

graph the line that passes through the points (0, -8) and (5, -5) and determine the equation of the line.

Explanation:

Step1: Find the slope

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Here, \((x_1,y_1)=(0, - 8)\) and \((x_2,y_2)=(5,-5)\). So \( m=\frac{-5-(-8)}{5 - 0}=\frac{-5 + 8}{5}=\frac{3}{5} \).

Step2: Use slope - intercept form

The slope - intercept form of a line is \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. We know that the line passes through \((0,-8)\), so when \( x = 0 \), \( y=-8 \). Substituting \( x = 0 \), \( y=-8 \) and \( m=\frac{3}{5} \) into \( y=mx + b \), we get \(-8=\frac{3}{5}(0)+b\), so \( b=-8 \).

Step3: Write the equation

Substituting \( m=\frac{3}{5} \) and \( b = - 8 \) into \( y=mx + b \), the equation of the line is \( y=\frac{3}{5}x-8 \).
(For graphing: Plot the points \((0,-8)\) (the y - intercept) and \((5,-5)\). Then draw a straight line passing through these two points.)

Answer:

The equation of the line is \( y=\frac{3}{5}x - 8 \)