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?

Mar 9, 2018

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 $\left({x}_{1} = 2 , {y}_{1} = 0\right)$

y-intercept = -3 or the point is $\left({x}_{2} = 0 , {y}_{2} = - 3\right)$

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

$\frac{y - {y}_{1}}{{y}_{2} - {y}_{1}} = \frac{x - {x}_{1}}{{x}_{2} - {x}_{1}}$

$\frac{y - 0}{- 3 - 0} = \frac{x - 2}{0 - 2}$

$\frac{y}{-} 3 = \frac{x - 2}{-} 2$

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

Mar 9, 2018

$3 x - 2 y = 6$

Explanation:

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

$\frac{x}{a} + \frac{y}{b} = 1$

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

$\frac{x}{2} + \frac{y}{- 3} = 1$

or $3 x - 2 y = 6$