# Intercepts and the Cover-Up Method

## Key Questions

color(blue)("Horizontal line " x = a

color(purple)("Vertical line " y = b

#### Explanation: Refer table above.

$\text{Equation of a line in" color(red)("Intercept Form") "is given by}$

$\frac{x}{a} + \frac{y}{b} = 1 , \text{ where a in x-intercept and b the y-intercept}$

For a horizontal line, y = 0 or y/b = 0 and the equation becomes,

$\frac{x}{a} = 1 \text{ or } x = a$

Similarly, for a vertical line, x = 0 or x / a = 0 and the equation becomes,

$\frac{y}{b} = 1 \text{ or } y = b$

• I suppose that "cover-up" is a friendlier term for "setting a variable equal to zero," so if you are looking for the $x$-intercept of a line, then set $y$ equal to zero, and for $y$-intercept, set $x$-equal to zero.

Example

Let us find the $x , y$-intercepts of the line

$2 x + 3 y = 12$.

To find the $x$-intercept, set $y = 0$.

$\implies 2 x + 3 \left(0\right) = 12 \implies 2 x = 12 \implies x = 6$

So, the $x$-intercept is $6$.

To find the $y$-intercept, set $x = 0$.

$\implies 2 \left(0\right) + 3 y = 12 \implies 3 y = 12 \implies y = 4$

So, the $y$-intercept is $4$.

I hope that this was helpful.