Question

What is the equation of the line that contains (-4, -1) and (-8,-5)?

Answer 1

`y=1x+3`

Explanation:

Begin by finding the slope using the equation: `m=(y_2-y_1)/(x_2-x_1)`

If we let `(-4,-1)->(x_1,y_1)` and `(-8,-5)->(x_2,y_2)` then,

`m=((-5)-(-1))/((-8)-(-4))=-4/-4=1`

Now that we have the slope, we can find the equation of the line using the point-slope formula using the equation: `y-y_1=m(x-x_1)`
where `m` is the slope and `x_1` and `y_1` are the coordinates of a point on the graph.

Using `1` as `m` and the point `(-4,-1)` to be `x_1` and `y_1`, substituting these values into the point-slope formula we get:

`y-(-1)=1(x-(-4))`

`y+1=1(x+4)`

We can rewrite the equation above in `y=mx+b` form by solving for `y`:

`y+1color(red)(-1)=1x+4color(red)(-1)`

`y=1x+3`