Summary
This math recipe will help you find the equation of a line, in the XY plane, whose intercepts are given.
Skill Level
Easy
Time
Approx. 1 min
Ingredients
x-intercept of the line: a
y-intercept of the line: b
Method
To find the equation of the line, we’ll use the following:
x/a + y/b = 1
Examples
Example 1 Find the equation of a line whose x-intercept is –3 and y-intercept is 4.
Solution To find the equation, we’ll use the above form directly.
x/(-3) + y/4 = 1
⇒ 4x – 3y + 12 = 0
The figure shows the line on the XY plane.
Example 2 Find the equation of a line whose x-intercept is 2 and y-intercept is –5
Solution To find the equation, we’ll use the above form directly.
x/2 + y/(-5) = 1
⇒ -5x + 2y + 10 = 0
The figure shows the line on the XY plane.
Example 3 Find the equation of a line whose x-intercept is 4 and y-intercept is infinite.
Solution To find the equation, let’s use the above form directly.
x/4 + y/b = 1
Since b is infinite, the term y/b becomes 0 (a somewhat crude argument). We’ll therefore get the equation as
x/4 = 1
⇒ x = 4
The figure shows the line on the XY plane.
That’s it for this recipe. Hope you found it helpful.
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