Question

Write the equation in the slope-intercept form, and then find the slope and \(y\) -intercept of the corresponding lines. $$ -3 x+4 y-8=0 $$

Short answer

The given equation can be rearranged into the slope-intercept form, resulting in \(y = \frac{3}{4}x + 2\). The slope (m) equals \(\frac{3}{4}\), and the y-intercept (b) equals 2.

Step-by-step solution

Rewrite the equation in slope-intercept form

First, we want to rearrange the given equation to highlight y and rewrite it in the slope-intercept form:\(-3x + 4y - 8 = 0\). Let's isolate y: 1. Add \(3x\) to both sides of the equation: \(4y = 3x + 8\). 2. Divide both sides by 4: \(y = \frac{3}{4}x + 2\). Now, the equation is in the slope-intercept form, \(y = mx + b\).

Identify the slope

In the slope-intercept form equation, \(y = \frac{3}{4}x + 2\), the coefficient of x, which is \(\frac{3}{4}\), represents the slope (m). Therefore, the slope of the line is \(\frac{3}{4}\).

Identify the y-intercept

In the slope-intercept form equation, \(y = \frac{3}{4}x + 2\), the constant term, which is 2, represents the y-intercept (b). Therefore, the y-intercept of the line is 2. So, the given equation in slope-intercept form is \(y = \frac{3}{4}x + 2\), and the corresponding slope m is \(\frac{3}{4}\), while the y-intercept b is 2.