which of the following are point-slope equations through the line of (-4,6) and (1,2)?(Two equations)?

Question

I'm not sure how to do the problem. Can you pleas provide and steps and answers?

Answer 1

Edit: While I was writing this, I saw that you got another answer from someone else. I guess I'll leave my answer here anyway, though, in case it helps haha.

 

Hi Kelly,

The first thing to do would be to figure out what "point-slope" is asking for. From what I know, it means the (linear) equation uses the slope of the line as well as a point on the line (hence the name).

So, we have to find the slope of the line. We are given two points, so we can use those:
(x1,y1) = (-4,6)
(x2,y2) = (1,2)
m = (y2-y1)/(x2-x1) = (2-6)/(1--4) = (2-6)/(1+4) = -4/5

Also, we know that point-slope is of the form:
(y-y1) = m*(x-x1)
It doesn't matter which point you use, though, you can also use:
(y-y2) = m*(x-x2)

So we can plug the variables into the equation and get:
(y-2) = -4/5*(x-1)
OR
(y-6) = -4/5*(x+4)

Multiplying out the two point-slope forms and simplifying give the same equation in slope-intercept form: y = mx+b.

Answer 2

Kelly, we don't see your equation. Meanwhile your slope is 6-2/-4-1=-4/5. With this you can have (y-6)/(x+4)=-4/5 as a point-slope equation. Or, you can have (y-2)/(x-1)=-4/5. hope this helps you