To graph this function, we follow the following steps:
Express the function in the Slope-Intercept form, y = ax + b. We make y the subject of the function
a. y = 2x + 3
when x = - 2
y = 2(-2) + 3 = - 4 + 3 = - 1
(x, y) = (-2, -1)
when x = 0
y = 2(0) + 3 = 0 + 3 = 3
(x, y) = (0, 3)
when x = 3
y = 2(3) + 3 = 6 + 3 = 9
(x, y) = (3, 9)
Slope = Δy / Δx = (9 - 3)/(3 - 0)
m = 6/3 = 2
The next step is to plot this values on a graph
b. -x + 4y = 12
Add x to both sides, we have:
4y = x + 12
Divide each element by 4, we have:
y = ¼x + 3
when x = -4
y = ¼(-4) + 3 = -1 + 3 = 2
(x, y) = (-4, 2)
when x = 0
y = ¼(0) + 3 = 0 + 3 = 3
(x, y) = (0, 3)
when x = 8
y = ¼(8) + 3 = 2 + 3 = 5
(x, y) = (8, 5)
Slope = Δy / Δx = (5 - 3)/(8 - 0)
m = 2/8 = 1/4