Question

How do you find the equation, x-intercept, and the y-intercept for the line with an x-intercept of 2, and y-intercept of -3?

Answer 1

Equation of the line is `color(green)(2y = 3x - 6`

Explanation:

The x-intercept is where a line crosses the x-axis. ie y = 0.

The y-intercept is where the line crosses the y-axis. ie x = 0.

Given : x-intercept = 2 or the point is `(x_1 = 2, y_1 = 0)`

y-intercept = -3 or the point is `(x_2 = 0, y_2 = -3)`

Knowing two points on the line, equation can be formed using

`(y - y_1) / (y_2 - y_1) = (x - x_1) / (x_2 - x_1)`

`(y - 0) / (-3 - 0) = (x - 2) / (0 -2)`

`y / -3 = (x - 2) / -2`

Equation of the line is `color(green)(2y = 3x - 6`

Answer 2

`3x-2y=6`

Explanation:

Equation of a line whose `x` intercept is `a` and `y`-intercept is `b` is

`x/a+y/b=1`

For details see here.

Hence equation of a line whose `x` intercept is `2` and `y`-intercept is `-3` is

`x/2+y/(-3)=1`

or `3x-2y=6`