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 )