Question
I'm having a hard time with coming up with equations. Here's an example:
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!
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!
Answers
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!
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!
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.
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.
Side note: Use post one as preview for post 2!
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!
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!
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