Question

Hi I need helping solving this practice problem Find the slopes of the lines.

Answer 1

The Slope of a line that passes through the points (x₁,y₁) and (x₂,y₂) is given by the formula:

`m=(y_2-y_1)/(x_2-x_1)`

Notice from the graph that the blue line passes through points (0,2) and (3,0).

Substitute (x₁,y₁)=(0,2) and (x₂,y₂)=(3,0) into the slope formula:

`m=(0-2)/(3-0)=-(2)/(3)`

Hence, the slope of the blue line is -2/3.

Notice from the graph that the green line passes through the points (1,-2) and (4,-4):

Substitute (x₁,y₁)=(1,-2) and (x₂,y₂)=(4,-4) into the slope formula:

`m=(-4-(-2))/(4-1)=(-4+2)/(3)=(-2)/(3)=-(2)/(3)`

Hence, the slope of the green line is -2/3.

The slope of both lines is -2/3.