Question

Enter an equation in point-slope form for the line. (6,8) and (7,1) is on the line. The equation of the line in point slope form is:

Answer 1

`y - 8 = -7(x - 6)` or
`y - 1 = -7(x - 7)`

Explanation:

The point-slope form equation is
`y - b = m(x - a)`, where,

(a, b) = a point on the line.

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

Given the two points, (6, 8) and (7, 1), find the slope of the line:

`m = (1 - 8)/(7 - 6)`

`m = (-7)/(1)`

`m = -7`

There are two possible point-slope equation we can come up with using each points on the line given.

Using the point (6, 8) and m = -7,

Substitute m = -7, a = 6, and b = 8 into
`y - b = m(x - a)`

`y - 8 = -7(x - 6)`

Using the point (7, 1) and m = -7,

Substitute m = -7, a = 7, and b = 1 into
`y - b = m(x - a)`

`y - 1 = -7(x - 7)`