Question

enter the correct answer that completes the sentence below. any line parallel to the graph of 4x + 7y = 4 must have the slope \square. (type an integer or a simplified fraction.)

Explanation:

Step1: Rewrite the equation in slope - intercept form

The slope - intercept form of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. We start with the equation \(4x+7y = 4\).
First, we isolate \(y\) on one side of the equation. Subtract \(4x\) from both sides: \(7y=-4x + 4\).
Then, divide each term by \(7\): \(y=-\frac{4}{7}x+\frac{4}{7}\).

Step2: Determine the slope of parallel lines

Parallel lines have the same slope. For the line \(y =-\frac{4}{7}x+\frac{4}{7}\), the slope \(m =-\frac{4}{7}\). So any line parallel to \(4x + 7y=4\) will have the same slope.

Answer:

\(-\frac{4}{7}\)