equation for the line that passes through (0,15) and (5,3)?

Question

also line that passes through (-2,2) and (5,-4)

Answer 1

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We want y = mx + b for a line that passes through (0,15) and (5,3).

m is the slope, which is the rise (difference in Y values) divided by the run (difference in X values).

(3-15) / (0-5) = -12/-5 = 12/5

So m = 12/5

y = (12/5)x + b

Now, to find b, we have to plug in one of our points for x and y, and solve the equation for b:

15 = (15/5)0 + b

15 = b

So the first line equation is:

y = (12/5)x + 15

Do the same thing for the other line...

y = mx + b

m = (-4 - 2) / (5 - -2)

m = -6 / 7

y = (-6/7)x + b

2 = (-6/7)*-2 + b

2 = 12/7 + b

14/7 - 12/7 = b

2/7 = b

Therefore, y = (-6/7)x + 2/7