Question

What is the equation of the line passing through the points `(-5, 14)` and `(4, -4)`?

Answer 1

`y=-2x+4`

Explanation:

Use the slope formula:

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

Given `(-5,14)` and `(4,-4)`

Let:

`(color(red)(-5),color(blue)(14))->(color(red)(x_1),color(blue)(y_1))`

`(color(red)(4),color(blue)(-4))->(color(red)(x_2),color(blue)(y_2))`

Substituting in for the slope formula...

`m=color(blue)(-4-14)/color(red)(4-(-5))=color(blue)(-18)/color(red)(9)=-2`

Now that we have the slope `m`, we can find the equation of the line by using the point-slope formula:

`y-y_1=m(x-x_1)`

Note: `(x_1,y_1)` can be either point given. I'll use the point `(4,-4)`

So...

`y-(-4)=-2(x-4)`

`y+4=-2(x-4)`

We can then rewrite this equation in `y=mx+b` form by simply solving for `y`

Doing so, one gets,

`y=-2x+4`