What is the Slope intercept form of (4,9) and (-2,5), and what is the standard form of it?

Answer 1

Standard slope-intercept form is y(x) = mx + b where m is the slope and b the y-intercept
Take each point separately:
y(4) = m(4) + b = 9
y(-2) = m(-2) + b = 5
Subtract the second from the first:
m(4--2) = 9-5 = 4
2m = 4, m = 2
y(x) = 2x + b
y(4) = 2(4) + b = 9
b = 9-8 = 1
y(x) = 2x + 1

Answer 2

Slope intercept form is y = mx + b where m is the slope and b is the intercept.

Standard form is ax + by = c

Slope intercept form:

m = (5 - 9) / (-2 - 4) = (-4)/(-6) = 2/3

y = mx + b = (2/3)x = b
Take the second point and substitute it into this equation.
5 = (2/3)(-2) + b
b = 19/3

y = (2/3)x + 19/3

Check using the other point:
9 = (2/3)4 + 19/3 = 8/3 + 19/3 = 27/3 = 9 So the answer is good.

Standard form. Start with the slope-intercept form and put the x and y on one side.

y = (2/3)x + 19/3
(2/3)x - y = -19/3
2x - 3y = -19