Question

Write the equation of a line in slope intercept form that passes through the two points. 4,-1 and 6,-7

Answer 1

A line has an equation of,

$y=mx+n$.

m is called a slope

n is called y-intercept

We are also given two points $(x_1,y_1)=(4,-1),(x_2,y_2)=(6,-7)$.

We begin with computing the slope,

$m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{-7-(-1)}{6-4}=\frac{-7+1}{2}=\frac{-6}{2}=\boxed{-3}$

We have computed the slope m and our equation is almost done,

$y=-3x+n$

Next step is to find out what y-intercept n is. I will use point $(4,-1)$ and insert x and y it into already known equation, then solve for n,

$-1=-3(4)+n$

$-1=-12+n\implies n=\boxed{11}$

The reason I can insert coordinates of a point as x and y is because this particular point is in the line described by equation,

$\boxed{y=-3x+11}$

Hope this helps. :)