Question

Write an equation of the line in slope-intercept form passing through the points (-2,3) and (2,-5)

Answer 1

We are asked to find the equation of the line in slope-intercept form that passes through the following points.

`(-2,3)\: \text{and }(2,-5)`

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 y-intercept is the point when the line crosses the y-axis.

The slope of the line is given by

`m=(y_2−y_1)/( x_2−x_1)`
`\text{where}(x_1,y_1)=(-2,3)\text{and}(x_2,y_2)=(2,-5)`

Let us substitute the given values into the slope formula

`m=(-5-3)/(2-(-2))=(-8)/(2+2)=(-8)/(4)=-2`

So the equation of line becomes

`y=-2x+b`

Now let us find the y-intercept (b)

Choose any one point from the given two points

Let's choose (-2, 3) and substitute it into the above equation

`\begin{gathered} y=-2x+b \\ 3=-2(-2)+b \\ 3=4+b \\ b=3-4 \\ b=-1 \end{gathered}`

Please note that even if you had chosen the other point then still you would have gotten the same y-intercept.

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

`y=-2x-1`