Question

Find the equation of the line that passes through the points $(-1,0)$ and $(-4,12)$

• A. $y+4x=-1$
• B. $y+4x=-4$
• C. $-y+4x=-8$
• D. $y-8x=-12$

Answer 1

Answer: (B)

$y+4x=-4$

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 $(-1,0)$ and $(-4,12)$ as shown below:

$m=\frac{12-0}{-4-(-1)}=\frac{12}{-3}=-4$

Therefore, the slope of the line is $-4$.

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

$y=mx+b$

$0=(-4)(-1)+b$

$0=4+b$

$b=-4$

Write the equation in slope intercept form as:

$y=mx+b$

$y=(-4)x-4$

$y=-4x-4$

$y+4x=-4$

Hence, the equation of the line is $y+4x=-4$.