Question

Point-slope form of an equation of the line through the points (-1, 4) and (-2, 2). ​

Answer 1

y - 4 = 2(x + 1)

or

y - 2 = 2(x + 2)

Explanation:

The point-slope of an equation of a line:

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

m - slope

The formula of a slope:

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

We have the points (-1, 4) and (-2, 2).

Substitute:

`m=(2-4)/(-2-(-1))=(-2)/(-1)=2`

for the point (-1, 4):

`y-4=2(x-(-1))\\\\y-4=2(x+1)`

for the point (-2, 2):

`y-2=2(x-(-2))\\\\y-2=2(x+2)`

Answer 2

The point-slope form equation of a line is: y − y1 = m(x − x1)

First find the slope which is the change in y over the change in x:

Slope = 2-4 / -2 - -1 = 2-4 / -2+1 = -2/-1 = 2

In the point-slope equation:

M = slope = 3

y1 = 4

x1 = -1

Replace the letters with their values to get:

y -4 = 2(x- -1)

Simplify:

Point-slope form: y-4 = 2(x+1)