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

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

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- 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##