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Find an equation of the line that satisfies the given conditions. x-intercept = -8; y-intercept ...

Question:

Find an equation of the line that satisfies the given conditions. x-intercept = -8; y-intercept = 2.

Intercept Form:

The intercepts of a line are the points where the line meets the x-axis and the y-axis. If {eq}(a,0) {/eq} and {eq}(0,b) {/eq} are the intercepts of a line then its equation is found by using: {eq}\dfrac{x}{a}+ \dfrac{y}{b}=1 {/eq}.

Answer and Explanation:

The intercepts of the line are:

$$\text{x-intercept is}, a =-8 \\ \text{y-intercept is}, b=2 $$

The equation of a line in the intercept form is:

$$\dfrac{x}{a}+ \dfrac{y}{b}=1 \\[0.3cm] \dfrac{x}{-8}+ \dfrac{y}{2}=1 \\[0.3cm] \text{Multiply each term on both sides by -8}, \\[0.3cm] x - 4y = -8 \\[0.3cm] \text{Subtracting x from both sides}, \\[0.3cm] -4y=-x-8 \\[0.3cm] \text{Dividing both sides by -4}, \\[0.3cm] \boxed{\mathbf{y= \dfrac{1}{4}x +2}} $$


Learn more about this topic:

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Linear Equations: Intercepts, Standard Form and Graphing

from Math 101: College Algebra

Chapter 1 / Lesson 4
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