Question

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

Answer 1

Answer:

$y+1=3x$

OR

$y-2=3(x-1)$

Step-by-step 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)

$m=\displaystyle \frac{y_2-y_1}{x_2-x_1}$ 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):

$m=\displaystyle \frac{2-(-1)}{1-0}\\\\m=\displaystyle \frac{2+1}{1}\\\\m=3$

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!