Question

For the points (1, -4) and (-2, -10), find the slope-intercept equation of the line passing through the points.
I know the equation is y=mx+b and that m=2, but I don't know which numbers to plug in and where.

Answer 1

\[\frac{y - y_1}{x-x_1} = \frac{y_2-y_1}{x_2-x_1}\]
Put \((x_1, y_1) = (1, -4) \) and \((x_2, y_2) = (-2, -10)\) into the formula.
\[\frac{y - (-4)}{x-(1)} = \frac{-10-(-4)}{(-2)-(1)}\]\[\frac{y+4}{x-1} = \frac{-6}{-3}\]\[\frac{y+4}{x-1} = 2\]\[y+4 = 2(x-1)\] Now simplify it.

Special note: As you can see, the right side of the formula is actually finding the slope of the line :)

Answer 2

This is pretty confusing >< Sorry.

Answer 3

Hmm?! Which part??
No worries btw :)

Answer 4

My professor taught it a different way, I think. I just can't find my notes.

Answer 5

I remember it was a linear equation (no fractions)

Answer 6

\(y - y_1 = m (x-x_1)\)???

Answer 7

Yeah, that was it! I just found my notes :P (I see that your way works, too. But, I have a final tomorrow. I don't want to have to learn something and unlearn something else last minute. Again, sorry)

Answer 8

never mind :)
It's just the same though :P
How do you find m generally with 2 points \((x_1, y_1)\) and \((x_2, y_2)\) given?

Answer 9

The rise/run equation. m= (y2-y1)/(x2-x1)

Answer 10

Yes. So, put m = (y2-y1)/(x2-x1) into y-y1 = m (x-x1)
You'll get
\[y-y_1 = \frac{(y_2-y_1)}{(x_2-x_1)} (x-x_1)\]Now divide both sides by (x-x1), what will you get?

Answer 11

Is the final answer y=2x-6?

Answer 12

Yes, I think.

Actually, I was trying to tell you that it's not something new. You just have to combine what you've learn and change a little to get that. Anyway, use the method you're comfortable at - This is the best for you when you do your exam. Good luck!

Answer 13

Thank you so much for your help! :)

Answer 14

Welcome :)