Question

graph the line that represents this equation. 5 - 4y = 6

Explanation:

Step1: Rewrite the equation in slope - intercept form

The given equation is \(5x - 4y=8\). We want to solve for \(y\) to get it in the form \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept.
First, subtract \(5x\) from both sides: \(-4y=-5x + 8\).
Then, divide each term by \(-4\): \(y=\frac{5}{4}x-2\).

Step2: Find the \(y\) - intercept

The \(y\) - intercept \(b=-2\), so the line passes through the point \((0, - 2)\).

Step3: Find another point using the slope

The slope \(m = \frac{5}{4}\), which means for a run of \(4\) (change in \(x\)), the rise is \(5\) (change in \(y\)). Starting from \((0,-2)\), if we move \(4\) units to the right (increase \(x\) by \(4\)) and \(5\) units up (increase \(y\) by \(5\)), we get the point \((0 + 4,-2+5)=(4,3)\).

Step4: Graph the line

Plot the points \((0,-2)\) and \((4,3)\) on the coordinate plane and then draw a straight line through them.

(Note: Since this is a graphing problem, the final answer is the graph of the line \(y=\frac{5}{4}x - 2\) passing through \((0,-2)\) and \((4,3)\) (and other points on the line). If we were to describe the key points: the \(y\) - intercept is \((0,-2)\) and another point is \((4,3)\).)

Answer:

The line is graphed by plotting the points \((0, - 2)\) (from \(y\) - intercept) and \((4,3)\) (using slope \(\frac{5}{4}\)) and drawing a straight line through them. The equation of the line in slope - intercept form is \(y=\frac{5}{4}x - 2\).