The rate of change of a line is equivalent to its slope.
The slope (m) of the line that passes through the points (x₁, y₁) and (x₂, y₂) is calculated as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
The line graphed passes through the points (-5, 0) and (0, -5), then its slope is:
[tex]m=\frac{-5-0}{0-(-5)}=-1[/tex]
The line of table A passes through the points (6, 11) and (10, 17), then its slope is:
[tex]m=\frac{17-11}{10-6}=\frac{3}{2}[/tex]
The line of equation B has the slope-intercept form:
[tex]y=mx+b[/tex]
with m = -3/2 (the slope) and b = -1.
The line of equation D also has the slope-intercept form with m = 1/2, and b = 3.
The line of table C passes through the points (3, 1) and (7, -3), then its slope is:
[tex]m=\frac{-3-1}{7-3}=-1[/tex]
which is the same slope (rate of change) as the function graphed
