Question

Calculate the rate of change over the interval of -10 < x < -6 of the graph.

Answer 1

The rate of change over the interval of -10 < x < -6 of the graph is 2

Explanation:

• The rate of change of a linear relation is the slope of the line

• The rule of the slope is
  `m=(y2-y1)/(x2-x1)` , 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

∴
`m=(2-(-6))/(-6-(-10))=(2+6)/(-6+10)=(8)/(4)=2`

∴ 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