Intercepts and the Cover-Up Method

Key Questions

What are the intercepts for horizontal and vertical line graphs?

Answer:

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

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

Explanation:

Refer table above.

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

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

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

$\frac{x}{a} = 1 or x = a$ $x / a = 1 " or " x = a$

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

$\frac{y}{b} = 1 or y = b$ $y / b = 1 " or " y = b$

sankarankalyanam · 1 · Apr 14 2018
How do you use the cover-up method to solve for the x and y intercept?

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

Example

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

$2 x + 3 y = 12$ $2x+3y=12$ .

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

$\Rightarrow 2 x + 3 (0) = 12 \Rightarrow 2 x = 12 \Rightarrow x = 6$ $=> 2x+3(0)=12 => 2x=12 => x=6$

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

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

$\Rightarrow 2 (0) + 3 y = 12 \Rightarrow 3 y = 12 \Rightarrow y = 4$ $=> 2(0)+3y=12 => 3y=12 => y=4$

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

I hope that this was helpful.

Wataru · 1 · Nov 2 2014

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Intercepts and the Cover-Up Method

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Graphs of Linear Equations and Functions