Question

question what is an equation of the line that passes through the point (-4,0) and is parallel to the line 5x - 4y = 20?

Explanation:

Step1: Find the slope of the given line

The given line is \(5x - 4y=20\), rewrite it in slope - intercept form \(y = mx + b\) (where \(m\) is the slope).
\[

$$\begin{align*} -4y&=-5x + 20\\ y&=\frac{5}{4}x-5 \end{align*}$$

\]
The slope \(m=\frac{5}{4}\).

Step2: Use the point - slope form for the new line

The point - slope form of a line is \(y - y_1=m(x - x_1)\), where \((x_1,y_1)=(-4,0)\) and \(m = \frac{5}{4}\).
\[

$$\begin{align*} y-0&=\frac{5}{4}(x + 4)\\ y&=\frac{5}{4}x+5\\ 5x-4y&=- 20 \end{align*}$$

\]

Answer:

\(5x - 4y=-20\)