Question

Which can be the first step in finding the equation of the line passing through (5,-4) and (-1,8)

Answer 1

The equation of the line, in slope-intercept form, is written as

`y=mx+b`

wherein m is the slope of the line and b is the y-intercept.

The first step to solve the equation of the line that passes through two points is to find the slope of the line given two points. The slope of the line can be computed using the equation

`m=(y_2-y_1)/(x_2-x_1)`

For points (5, -4) and (-1, 8), the slope of the line is

`m=(8-(-4))/(-1-5)=(12)/(-6)=-2`

Now, we have the initial equation of the line written as

`y=-2x+b`

To solve for the value of b, we use one of the points and substitute it on the initial equation above. In my case, I will be using points (5,-4), we have

`\begin{gathered} -4=-2(5)+b \\ -4=-10+b_{} \\ b=10-4 \\ b=6 \end{gathered}`

Hence, the equation of the line that passes through (5,-4) and (-1,8)​ is

`y=-2x+6`