Question

Which of the following is a point-slope equation of a line that passes through the points (-1,4) and (8,-2)

Answer 1

y = (2/3)x + 4 2/3

Explanation:

For reference, a linear function has an equation of y = mx + b

The first thing we're going to do is use the slope formula,
`(y2-y1)/(x2-x1)` or rise over run. In this case that looks like:

(-2-4) - (8 - -1)

-2 -4 comes out to - 6, and the denominator comes out to 9.

6/9 is equal to 2/3, which is our m or slope value.

Next we want to find the b value, or our y-intercept. To do that we'll plug one of the points into the equation with our new-found slope:

4 = (2/3)-1 +b

4 = -2/3 + b

4 2/3 = b

That means our complete equation is:

y = (2/3)x + 4 2/3

OR

y = (2/3)x + 14/3 (equivalent but an improper fraction rather than a mixed fraction).