Write the equation of the line with x-intercept 3 and y-intercept 2.

a) y = 2 3 x + 2
b) y = 3 2 x + 2
c) y = − 2 3 x + 2
d) y = − 3 2 x + 2

y=−23x+2

explanation:

by definition the x-intercept of 3 is the point (3, 0) and

by definition the y-intercept of 2 is the point (0, 2).

because we have two points we can use the point-slope formula to determine the equation. in order to use the point-slope formula we must first determine the slope of the line.

the slope can be found by using the formula: m=y2=y1x2−x1

where m is the slope and (x1,y1) and (x2,y2) are the two points.

substituting the two points from the problem gives the slope as:

m=0−23−0

m=−23

now that we have the slope we can use the point-slope formula to determine the equation of the line:

the point-slope formula states: (y−y1)=m(x−x1)

where m is the slope and #(x_1, y_1) is a point the line passes through.

we can substitute the slope we calculated and one of the points to give:

y−0=−23(x−3)

y=−23x+23⋅3

y=−23x+2answer:

step-by-step explanation:

y=mx+b is the final answer!   : )