Question

Find the point-slope equation of the line with slope -3 that passes through the point (2, -10).

Answer 1

Answer:

Step-by-step explanation

(-y-y1)/(x-x1)= m

y-(-10)/(x-2)= -3

y= -3x -4

Answer 2

Answer:

$y+10=-3(x-2)$

Step-by-step explanation:

First we must know the format of point-slope form.

This would be: $y-y1 = m (x-x1)$

Given x = 2, y = -10, and that our slope MUST be -3

Lets solve for "b" in the slope-intercept form using the variables provided to us. Remember that slope-intercept form is: $y=mx+b$  where "m" is the slope.

-10 = -3(2) + b

-10 = -6 + b

-4 = b

Congrats! We now have our b variable, which means we can write out our slope-intercept form for our equation. This would be:  $y=-3x-4$

We aren't done though, we now must convert this into point-slope form! Remember that x = 2 and y = -10

Lets plug in -3 for the "m" spot, -10 for the "y1" spot, and 2 for the "x1" spot in the point-slope equation.

$y+10=-3(x-2)$

(Why are we adding 10 instead of subtracting you might ask? Remeber that two negatives equal a positive; when we plugged in -10 into the "y1" spot it was already negative, it would essentially be this:  $y - (-10)$  which turns into a positive!)

Huzzah! We now have our equation in point-slope form which is equivalent to: $y=-3x-4$

Feel free to check on the Desmos graphing calculator if you wish!

If you have any questions feel free to ask! Hope this helped!