I'm having a hard time with coming up with equations. Here's an example:

Question

Complete the equation of the line through (−8,−2)and (−4,6)
Could anyone solve this and explain (as simple as possible) how you came up with the answer?
I'm sorry if this was a stupid question to ask but I'm having a really hard time with these types of things right now.
Thank you!

Answer 1

Well lets see!

Formula for a line is y = mx+b

(-8,-2) ==> x = -8 and its corresponding y is -2.
(-4, 6) ==> x = -4 and its corresponding y is 6.

Okay now, we must the slope formula, which is:

m = (y2 - y1) / (x2 - x1)

Using this formula you find your slope (which is your m).

Now put your value for m in the equation for the line (y = mx + b).

Now such choose one set of the points you provides and plug in its x value for the x in the equation, which already has your m (slope) in it (y = mx + b) and its corresponding y value. Now just solve for your b (y = mx+ b)

After that you are done! Congrats!

Answer 2

Solved:
So you take the coordinates and choose one set to be your (x1,y1) and the other one to be (x2,y2):

m = (6 - (-2)) / (-4-(-8)) = (8) / 4 = 2

Now plug in your m in this formula as shown:

y = mx + b = 2x+b

Now you must just choose either (-8,-2) or (-4,-6) as your x and corresponding y value and plug it in the formula above to find your b!

I will go for (-8,-2):

-2 = 2(-8) +b
-2 = -16 + b
-2 + 16 = b
14 = b

The final form would be y = 2x + 12

P.S. There is no such thing as a stupid question in math! Also good question and I commend your straightforwardness and your willingness to understand this concept better.

Answer 3

Side note: Use post one as preview for post 2!

Answer 4

slope = (6-(-2))/(-4-(-8) = 2
using the point (-4,6)

y-6 = 2(x+4)
y-6 = 2x + 8
y = 2x + 14

to check, sub both given points into this equation.
Both points work!