Write an equation in slope-intercept form of the line that passes through the points (-4,2) and (1,-1).

Question

mathstudent55 · Answer

Slope intercept form is

$y = mx + b$

mathstudent55 · Answer

m = slope
b = y-intercept

mathstudent55 · Answer

Since you are given two points on the line, you can find the slope.

mathstudent55 · Answer

The slope, $m$, of the line that passes through points $(x_1, ~y_1)$ and $(x_2, ~y_2) $ is

$m = \dfrac{y_2 - y_1}{x_2 - x_1} $

anonymous · Answer

I tried to solve it and I got Y=-12x-10. But that's not the right answer.

mathstudent55 · Answer

What did you get for the slope?

anonymous · Answer

m=-3

mathstudent55 · Answer

Let's do the slope:

$m = \dfrac{y_2 - y_1}{x_2 - x_1}$

$m = \dfrac{-1 - 2}{1 - (-4) } = \dfrac{-3}{5} = -\dfrac{3}{5}$

This is what I get for slope.

anonymous · Answer

Your right, I messed up. I put 1-4 instead of 1-(-4). Would the answer be y=-\frac{ 12 }{ 5 }x-\frac{ 2 }{ 5 }

anonymous · Answer

I mean y=12/5x-2/5

mathstudent55 · Answer

Ok, now that we know the slope is -3/5, we can replace m with -3/5:

$y = -\dfrac{3}{5}x + b$

Now all we need to do is find b.

To do that just substitute x and y with the x- and y-coordinates of one known point and solve for b.
We know two points, (-4, 2) and (1, -1).

Let's use the fist point, (-4, 2).

$y = -\dfrac{3}{5} x + b$

$2 = -\dfrac{3}{5} \times (-4) + b$

$2 = \dfrac{12}{5} + b$

$2 - \dfrac{12}{5} = b$

$\dfrac{10}{5} - \dfrac{12}{5} = b$

$- \dfrac{2}{5} = b$

Now that we know b, we can write the slope-intercept form using the values we have for m and b:

$y = -\dfrac{3}{5}x - \dfrac{2}{5} $