Answer: y = 2x+6
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Explanation:
We'll need the slope first
m = slope
m = (y2-y1)/(x2-x1)
m = (0-(-4))/(-3-(-5))
m = (0+4)/(-3+5)
m = 4/2
m = 2
The slope is 2.
Next, pick either of the two given points to play the role of [tex](x_1,y_1)[/tex]
Let's say we picked on (-5,-4). The order doesn't matter so you could easily pick the other point as well.
We'll plug these items into the point slope equation below to solve for y.
[tex]y - y_1 = m(x - x_1)\\\\y - (-4) = 2(x - (-5))\\\\y + 4 = 2(x +5)\\\\y + 4 = 2x +10\\\\y = 2x +10-4\\\\y = 2x +6\\\\[/tex]
Or we could have picked on (-3,0). The m value stays the same (at m = 2)
[tex]y - y_1 = m(x - x_1)\\\\y - 0 = 2(x - (-3))\\\\y = 2(x +3)\\\\y = 2x+6\\\\[/tex]
This one takes a few less steps. Either way, we get to the same answer.
You only need to pick one of the points, but doing both of them helps show that the two points are on the same line. It helps confirm the answer.
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Another way to check the answer is to plug the (x,y) coordinates into y = 2x+6 for each point.
So let's say we check (x,y) = (-5,-4)
y = 2x+6
-4 = 2(-5)+6 ... replace x with -5, replace y with -4
-4 = -10+6
-4 = -4
This confirms the first point. I'll let you check the second point.
