The Slope of a line that passes through the points (x₁,y₁) and (x₂,y₂) is given by the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
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:
[tex]m=\frac{0-2}{3-0}=-\frac{2}{3}[/tex]
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:
[tex]m=\frac{-4-(-2)}{4-1}=\frac{-4+2}{3}=\frac{-2}{3}=-\frac{2}{3}[/tex]
Hence, the slope of the green line is -2/3.
The slope of both lines is -2/3.
