Answer: [tex]y = \frac{1}{3}x-2[/tex]
This is the same as writing y = (1/3)x - 2
Slope = 1/3
y intercept = -2
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Explanation:
We first need to determine the slope
[tex]m = \frac{y_2-y_1}{x_2-x_1}\\\\m = \frac{-3-3}{-3-15}\\\\m = \frac{-6}{-18}\\\\m = \frac{1}{3}\\\\[/tex]
Then we'll use this value of m, along with (x,y) = (15,3), to determine the y intercept b value.
[tex]y = mx+b\\\\3 = (1/3)(15)+b\\\\3 = 5+b\\\\3 - 5 = b\\\\-2 = b\\\\b = -2[/tex]
You could use the other point (-3,-3) as well
[tex]y = mx+b\\\\-3 = (1/3)(-3)+b\\\\-3 = -1+b\\\\-3 +1 = b\\\\-2 = b\\\\b = -2[/tex]
Either way, we end up with the same y intercept. You don't need to show both sets of steps when computing b. You only need to pick one set of steps.
Since m = 1/3 and b = -2, we go from y = mx+b to y = (1/3)x - 2 which is the same as writing [tex]y = \frac{1}{3}x-2[/tex]
