Use the slopes of UQ, UR, US, and UT to estimate the rate of change of y at the specified value of x.
-$x= 5$

A) $\frac { 25 } { 4 }$
B) $\frac { 5 } { 2 }$
C) $\frac { 5 } { 4 }$
D) 0

Question

Use the slopes of UQ, UR, US, and UT to estimate the rate of change of y at the specified value of x.
-$x= 5$

A) $\frac { 25 } { 4 }$ 
B) $\frac { 5 } { 2 }$ 
C) $\frac { 5 } { 4 }$ 
D) 0

Quizplus · Accepted Answer

Using the slopes of each line:

- Slope of UQ: $\frac{-3-3}{4-3}=-6$ 
- Slope of UR: $\frac{7-3}{6-4}=2$ 
- Slope of US: $\frac{9-7}{8-6}=1$ 
- Slope of UT: $\frac{-1-9}{10-6}=-2$

The rate of change of y at x=5 is equal to the slope of the line that passes through the point (5, y) and is closest to the four given lines. Since the slope of UR is closest to the other three slopes, we choose its value, which is 2. Therefore, we have that the rate of change of y at x=5 is 2.

Use the Slopes of UQ, UR, US, and UT to Estimate