f(-1)= -3 is (-1,-3) and f(2) = 6 is (2,6) where f(x) = y
y=mx + b is the slope-intercept form whereas m equals the slope (rate of change) and b equals the y-intercept (initial amount/what y is when x is 0.)
First, we need to find the slope between the two points (-1,-3) and (2,6). To find the slope we could use one of it's formulas [tex] \frac{y^2 - y^1}{x^2 - x^1} [/tex].
1. (-1,-3)
2. (2,6)
[tex] \frac{6 - -3}{2 - -1} [/tex] → [tex] \frac{9}{3} [/tex] → [tex] \frac{3}{1} [/tex]
The slope is 3 ([tex] \frac{3}{1} [/tex]). Thusly, y = 3x + b
To find out the y-intercept, we can reverse the slope. [Note: This [tex] \frac{3}{1} [/tex] is in [tex] \frac{rise}{run} [/tex] where rise is 'y' and run is 'x'. Reversed would be [tex] \frac{-3}{-1} [/tex] ]. Take the second ordered pair and use our reversed slope on it until we get 0 for x.
(2, 6) ⇒ (2 - 1, 6 -3) ⇒ (1, 3) ⇒ (0,0)
Y-intercept is 0. Therefore, y= 3x + 0 [NOTE: y = f(x), so if you want it in function notation form it's just f(x) = 3x + 0.]
