Question

What is the equation of the line, in slope-intercept form, that passes through (3, -1) and (-1, 5)?


y = -3/2x + 7/2
2y = -3x + 7
2x + 3y - 7 = 0

Answer 1

Hello @thedj4JC ! Do you know the slope formula?

Answer 2

No, I don't

Answer 3

The slope formula is a very useful tool that helps you find the slope of a line. If you know the slope and a point the line passes through, you can find the equation of the line. So, very handy.
If a line passes through two points \((x_1,y_1)\) and \((x_2,y_2)\), the slope of that line equals...
\(\Large\frac{y_2-y_1}{x_2-x_1}\)

Answer 4

Remember that yours points are (3.-1) and (-1.5). Can you find the slope of the line?

Answer 5

It'd be
-1-5/3-(-1)?
-6/4?

Answer 6

-1.5??

Answer 7

Yeah, -6/4 is correct. nice job. But you should reduce it.

Answer 8

-6/4 = -3/2

Answer 9

So, next step. Now you want to find the equation of the line.
Slope-intercept form of a line: y = mx + b
m = slope

So, you get y = (-3/2)x + b
But we still don't know what b is. Luckily, we know that point (3, -1) goes through the line. Remember that a coordinate is in form (x,y). So, that means you can plug in 3 for x and -1 for y into the equation and solve for b. can you do that?

Answer 10

To solve for b, just substrate mx ((-3/2)3) from y (-1)?

Answer 11

y = mx + b

We know the slope
y = (-3/2)x + b

We have point (3, -1)
(-1) = (-3/2)(3) + b

Now solve for b

Answer 12

(-3/2)(3) = - 4 1/2
-1 - (-4 1/2) = 7/2

Answer 13

Nice job. Now just plug in the slope and the b-value back in...
y=mx + b
m = -3/2, b = 7/2
\(\Large y=-frac{3}{2}x+\frac{7}{2}\)
Now you've got your equation

Answer 14

Sorry, let me do that again

Answer 15

\(\Large y=- \frac{3}{2}x+\frac{7}{2}\)

Answer 16

Thank you!!!!

Answer 17

You're welcome! :)