How do you write an equation with X-intercept of 3 and y-intercept of 2?

1 Answer
smendyka
Dec 17, 2016

#y = -2/3x + 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: #color(red)(m = (y_2 = y_1)/(x_2 - x_1)#
Where #m# is the slope and #(x_1, y_1)# and #(x_2, y_2)# are the two points.

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

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

#m = -2/3#

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: #color(red)((y - y_1) = m(x - x_1))#
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 = -2/3(x - 3)#

#y = -2/3x + 2/3 * 3#

#y = -2/3x + 2#

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