Question

What is the equation of the line that passes through (-2, 2) and (1, -4)? y = -2 x - 4 y = -2 x - 2 y = 2 x - 2 y = 2 x + 4

Answer 1

Finding the equation of Slope Intercept Form by using 2 points.

First I'm going to take the two points to find the slope (or gradient) by using the formula m=y2-y1/x2-x1, you might also see it as m=Δy/Δx=y2-y1/x2-x1.

(-2,2), is the first point, so the x and y numbers given will be called x1 and y1, so you'll put them in the problem as x1=-2 and y1=2. Next, (1,-4), is the second point, so you'll do the same thing for that one, so instead of the one behind the variables put a two.

`m=(y_(2)-y_(1))/(x_(2) -x_(1) )\\\\m=(-4-2)/(1-(-2)) \\\\m=(-6)/(3) \\\\m=-2`

So now the equation is y=-2x+b, but where's the y-intercept? We're about to find out. To find the y-intercept take (x,y) and take out the x and y, then put it into the equation, so x&y are going to replace the variables in the equation y=-2x+b to find the y-intercept. YOU CAN USE EITHER POINT.

`2=-2(-2)+b\\\\2=4+b\\\\-2=b\\\\b=-2`

The equation of the line that passes through the points

(-2,2) and (1,-4) is y=-2x-2.

Hope this helps, HAVE A BLESSED AND WONDERFUL DAY! Also I hope you had a great Superbowl!