Question

Find an equation of the line that goes through the points (-10,13) and (-4,7). Write your answer in the formY=mx+b

Answer 1

`y=-x+3`

1) In this problem, let's plug those points into the slope formula to get the slope, i.e. the measure of how steep is the line between those points:

`m=(y_2-y_1)/(x_2-x_1)=(7-13)/(-4-(-10))=(-6)/(6)=-1`

2) Now, let's find the y-intercept, a.k.a. the linear coefficient "b". To do that we need to plug into the Slope-Intercept Formula one of those points, the slope, and solve it for "b"

`\begin{gathered} (-4,7),m=-1 \\ y=mx+b \\ 7=-4(-1)+b \\ 7=4+b \\ 7-4=b \\ b=3 \end{gathered}`

3) Therefore, the equation of the line is:

`y=-x+3`