Question

Find the equation of the line that passes through the points $(7,5)$ and $(-9,5)$

• A. $y=5$
• B. $y=5x+7$
• C. $5y=7x+5$
• D. $y=-5$

Answer 1

The correct option is A $y=5$

Since slope of line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2-y_1}{x_2-x_1}$

We now find the slope of the line passing through the points $(7,5)$ and $(-9,5)$ as shown below:

$m=\frac{5-5}{-9-7}=\frac{0}{-16}=0$

Therefore, the slope of the line is 0.

Now use the slope and either of the two points to find the $y$-intercept.

$y=mx+b$

$5=\left(0\right)\left(7\right)+b$

$b=5$

Write the equation in slope intercept form as:

$y=mx+b$

$y=\left(0\right)x+5$

$y=5$

Hence, the equation of the line is $y=5$.