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##