Chapter 11.3, Problem 4STP

For Exercises 1-4, choose the correct letter.

What coordinates satisfy the equation of the line $y=-\frac{7}{8}x+2$?

$F\left(-8,11\right)G\left(-4,\frac{11}{2}\right)HbothFandGI\left(4,\frac{11}{2}\right)$

To determine

To find the coordinate which satisfy the equation of the line

Answer to Problem 4STP

The correct answer is (G)

Explanation of Solution

Given information:

The equation of the line is $y=-\frac{7}{8}x+2$

The given answer is $\begin{array}{l}\left(\text{F}\right)\left(-8,11\right)\left(\text{G}\right)\left(-4,\frac{11}{2}\right)\\ \left(\text{H}\right)\text{ both F and G }\left(\text{I}\right)\left(4,\frac{11}{2}\right)\end{array}$

The coordinate which satisfy the equation of the line can be obtained as

  $y=-\frac{7}{8}x+2$

Put the value of $x=-8\text{ and }y=11$ on the above equation

  $\begin{array}{l}11=-\frac{7}{8}\left(-8\right)+2\\ 11=7+2\\ 11\ne 9\end{array}$

Again, put the value of $x=-4\text{ and }y=\frac{11}{2}$ on the equation of the line

  $\begin{array}{l}\frac{11}{2}=-\frac{7}{8}\left(-4\right)+2\\ \frac{11}{2}=\frac{28}{8}+2\\ \frac{11}{2}=\frac{28+16}{8}\\ \frac{11}{2}=\frac{44}{8}\\ \frac{11}{2}=\frac{11}{2}\left[\text{divide numerator and denominator by 4}\right]\end{array}$

The coordinate $\left(-4,\frac{11}{2}\right)$ satisfy the equation

Hence,

The correct answer is (G)