Question

What is anequation of the line that passes through the points (-4, -1) and(6, -1)?

Answer 1

We are given the following two points

$(-4,-1)\text{and }(6,-1)$

We are asked to find the equation of the line that passes through these points.

Recall that the equation of the line in slope-intercept form is given by

$y=mx+b$

Where m is the slope and b is the y-intercept.

The slope of the line is given by

$m=\frac{y_2−y_1}{ x_2−x_1}$$\text{where}(x_1,y_1)=(-4,-1)\text{and}(x_2,y_2)=(6,-1)$

Let us substitute the given values into the slope formula

$m=\frac{-1-(-1)}{6-(-4)}=\frac{-1+1}{6+4}=\frac{0}{10}=0$

So, the slope of the equation is 0

The equation of the line becomes

$y=0x+b$

Now let us find the y-intercept (b)

Choose any one point from the given two points

Let choose (-4, -1) and substitute it into the above equation

$\begin{gathered} y=0x+b \\ -1=0(-4)+b \\ -1=0+b \\ b=-1 \end{gathered}$

Therefore, the equation of the line in slope-intercept form is

$y=-1$

Note that this equation has 0 slope that is why mx part becomes 0