Chapter 11.3, Problem 3STP

For Exercises 1-4, choose the correct letter.

If a line passes through the points (2, 0) and (-2, -3), what is the y-intercept of the line? $A\frac{-3}{2}B\frac{3}{2}C\frac{3}{4}D\frac{-3}{4}$

To determine

To find the y -intercept of the line

Answer to Problem 3STP

The correct answer is (A)

Explanation of Solution

Given information:

The line passes through the point $\left(2,0\right)\text{ and }\left(-2,-3\right)$

The given answer is $\begin{array}{l}\left(\text{A}\right)-\frac{3}{2}\left(\text{B}\right)\frac{3}{2}\\ \left(\text{C}\right)\frac{3}{4}\left(\text{D}\right)\frac{-3}{4}\end{array}$

The y -intercept of the line can be obtained as

First we find the slopes of the line

  $m=\frac{y_1-y_2}{x_1-x_2}$

Put the value of $x_1=2,x_2=-2,y_1=0\text{ and }{y}_2=-3$ on the above equation

  $\begin{array}{l}m=\frac{0-\left(-3\right)}{2-\left(-2\right)}\\ m=\frac{0+3}{2+2}\\ m=\frac{3}{4}\end{array}$

The equation is $y=mx+c$

Again, put the value of $m=\frac{3}{4},x=2\text{ and }y=0$ on the above equation

  $\begin{array}{l}0=\frac{3}{4}\left(2\right)+c\\ c=-\frac{6}{4}\\ c=-\frac{3}{2}\left[\text{divide numerator and denominator by 2}\right]\end{array}$

The y- intercept is $-\frac{3}{2}$

Hence,

The correct answer is (A)