Complete the point-slope equation of the line through (0, -1) and (1, 2)

Question

asked Sep 21, 2022 219k views

1 Answer

Sangbok Lee · Answer 1 · 2022-09-27T16:26:13+0000

Answer:

y+1=3x

OR

y-2=3(x-1)

Explanation:

Hi there!

Point-slope form:
y-y_1=m(x-x_1) where m is the slope and
(x_1,y_1) is a point

1) Determine the slope (m)

$m=\displaystyle (y_2-y_1)/(x_2-x_1)$ where two points that fall on the line are
(x_1,y_1) and
(x_2,y_2)

Plug in the points (0,-1) and (1,2):

$m=\displaystyle (2-(-1))/(1-0)\\\\m=\displaystyle (2+1)/(1)\\\\m=3$

Therefore, the slope of the line is 3. Plug this into
y-y_1=m(x-x_1) :

y-y_1=3(x-x_1)

2) Plug a point into the equation

y-y_1=3(x-x_1)

Because we're given two points, there are two ways we can write the equation:

$y-y_1=3(x-x_1)y-(-1)=3(x-0)\\y+1=3x$

OR

$y-y_1=3(x-x_1)\\y-2=3(x-1)$

I hope this helps!