Question

What is the equation of the line, in slope-intercept form, that goes through the point `(-6,4)` with `m=-1/2`?

Answer 1

`y=-1/2x+1`

Explanation:

To start, slope-intercept form is `y=mx+b`
where `m` is the slope and `b` is the y-intercept.

However, when just given a point, (-6,4) ,and the slope, we need to use another form called point slope form.

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

Here, `y_1 = 4, and x_1` = `-6` (from the point given in the question),
and `m` is `-1/2`

Our equation is now: `" "y-4=-1/2(x+6)`

Next, we need to distribute the `-1/2(x+6)`

This yields `-1/2x-3`

With this, Our equation is now `y-4=-1/2x-3`

Our last step is to add 4 to both sides. (to isolate `y`)

We now get `y=-1/2x+1` and this is your answer in slope-intercept form.

Hope this helps!