y = mx + b
m is the slope
we can find the y-intercept by figuring out what b is, because...
if we pretend the slope of the line is 0 and put 0 in m...
y = 0x + b
y = b
and only one point is going to go through a point on the y-line - the y-intercept
all we have to do is find b
now, we can just use any points on this imaginary line using the table of values to put in the y and x portion of the equation
let's use (-2, 15) for example
y = mx + b
15 = m(-2) + b
or
15 = -2m +b
but we still need to find the slope (m) in order to solve the equation and get b (y-intercept)
so, we can take this equation to find what the slope
m = (y2 - y1) / (x2 - x1)
we need two points to solve this equation. let's use (1, 6) and (2, 3)
in this equation, y2 is the y of (2, 3), the second point, and y1 is the y of (1, 6), the first point.
y2 = 3
y1 = 6
similarly, x2 is the x of (2, 3), the second point, and x1 is the x of (1, 6), the first point.
x2 = 2
x1 = 1
let's put it in the equation
m = (y2 - y1) / (x2 - x1)
m = (3 - 6) / (2 - 1)
m = -3 / 1
m = -3
the slope, m, is -3
let's put it in the first equation, along with the random point we selected earlier (-2, 15).
y = mx + b
15 = -2m +b
15 = -2(-3) + b
15 = 6 + b
15 - 6 = 6 - 6 + b
9 = b
b = 9
the y-intercept is 9
so, A. :))
