Firstly lets shorten the equation with distributive law:
y-2= 4(3x + 5)
y-2 = 12x + 20
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
y-2-(12*x-20)=0
y=mx+b is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.
Calculate the y intercept:
Notice that when x = 0 the value of y is -18/1 so this line "cuts" the y axis at y=-18.00000
y-intercept = -18/1 = -18.00000
Calculate the x intercept:
When y = 0 the value of x is 3/2 Our line therefore "cuts" the x axis at x= 1.50000 x-intercept = 18/12 = 3/2 = 1.50000
Find the slope:
Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is -18.000 and for x=2.000, the value of y is 6.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 6.000 - (-18.000) = 24.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN) Slope = 24.000/2.000 = 12.000
Therefore:
Slope = 24/2 = 12
x-intercept = 18/12 = 3/2 = 1.5
y-intercept = -18/1 = -18
So it is linear.
