Answer:
The rate of change over the interval of -10 < x < -6 of the graph is 2
Step-by-step explanation:
- The rate of change of a linear relation is the slope of the line
- The rule of the slope is [tex]m=\frac{y2-y1}{x2-x1}[/tex] , where (x1, y1) and (x2, y2) are two points on the line
In the given figure:
The relation between x and y over the interval of -10 < x < -6, represented by a line, then the rate of change over this interval is the slope of the line
∵ The line passes through points (-10, -6) and (-6, 2)
∴ x1 = -10 and y1 = -6
∴ x2 = -6 and y = 2
→ Substitute them in the rule of the slope above
∴ [tex]m=\frac{2-(-6)}{-6-(-10)}=\frac{2+6}{-6+10}=\frac{8}{4}=2[/tex]
∴ The slope of the line = 2
∵ The rate of change = the slope of the line
∴ The rate of change over the interval of -10 < x < -6 of the graph is 2
