What is the x-intercept of the graph that is shown below? On a coordinate plane, a line goes through points (0, 2) and (3, 0).

Given the points:

(0, 2)

(3, 0)

x1= 0

x2 = 3

y1 = 2

y2= 0

Find the x-intercept.

In order to find the x-intercept, we must first write the equation in point-slope form, then write in slope-intercept form.

Point-slope form:

y - y1 =m(x -x1)

Formula for the slope-intercept form

y = mx + b

Solution:

Before we can write in point-slope form, we must first find the slope of the line, we can find the slope by using the slope formula.

m = y2 -y1 /x2 -x1

m= (0 -2)/(3 - 0)

m = -⅔

Substitute the given values of x1, m and y1 to the formula for the point-slope form.

y - 2 = -⅔ ( x - 0 )

In order to change to slope-intercept form, we simply need to distribute --⅔ to each value inside the parenthesis, and then transpose -2 to the other side of the equation. Hence, we must take note that in transposing a number, the sign changes.

y -2 = -⅔x

y= -⅔x + 2

In order to find for the x-intercept, we need to equate y as 0, then solve for x.

0 = -⅔x + 2

⅔x = 2

Multiply both sides by 3/2 which is the reciprocal of ⅔, in order to cancel out ⅔x, leaving behind x.

(3/2)(⅔x) = (3/2)(2)

x = 3

x-intercept = 3

Final answer:
x-intercept = 3