Question

graph the line with the equation $y = -\frac{3}{4}x + 5$.

Explanation:

Step1: Find the y - intercept

The equation is in slope - intercept form \(y = mx + b\), where \(b\) is the y - intercept.
For \(y=-\frac{3}{4}x + 5\), \(b = 5\). So, plot the point \((0,5)\) on the y - axis.

Step2: Use the slope to find another point

The slope \(m=-\frac{3}{4}\). The slope \(m=\frac{\text{rise}}{\text{run}}\). Here, \(\text{rise}=- 3\) and \(\text{run}=4\).
Starting from the point \((0,5)\), move 3 units down (because the rise is negative) and 4 units to the right. We get the point \((4,2)\).

Step3: Draw the line

Connect the points \((0,5)\) and \((4,2)\) with a straight line. Extend the line in both directions.

Answer:

Plot the point \((0,5)\) (y - intercept), then use the slope \(m =-\frac{3}{4}\) (move 3 units down and 4 units right from \((0,5)\) to get \((4,2)\)), and draw a straight line through these two points.