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Chapter 1: Problem 44

Write the equation in the slopeintercept form and then find the slope and \(y\) -intercept of the corresponding line. $$ 5 x+8 y-24=0 $$

Short Answer

Expert verified
The equation is rewritten in slope-intercept form as: \(y = -\dfrac{5}{8}x + 3\). The slope of the line is \(-\dfrac{5}{8}\) and the y-intercept is 3.

Step by step solution

01

Rewrite the equation in slope-intercept form

To rewrite the given equation \(5x + 8y - 24 = 0\) in slope-intercept form, we need to isolate y by following these steps: 1. Subtract 5x from both sides 2. Divide by 8
02

Subtract 5x from both sides

To subtract 5x from both sides of the equation, we have: \(8y = -5x + 24\)
03

Divide by 8

To isolate y, we need to divide by 8. So, we have: \(y = \dfrac{-5x}{8} + \dfrac{24}{8}\) Simplifying the equation, we get: \(y = -\dfrac{5}{8}x + 3\) Now that we have the equation in slope-intercept form, we can easily identify the slope and y-intercept.
04

Identify the slope

In the slope-intercept form, y = mx + b, m represents the slope. Comparing our equation with this form, we can see that the slope m = -\dfrac{5}{8}.
05

Identify the y-intercept

In the slope-intercept form, y = mx + b, b represents the y-intercept. Comparing our equation with this form, we can see that the y-intercept b = 3. So, the slope of the line is -\dfrac{5}{8} and the y-intercept is 3.

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