Question

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

Explanation:

Step1: Identify the slope and y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For the equation \(y=-\frac{3}{4}x + 5\), the slope \(m =-\frac{3}{4}\) and the y - intercept \(b = 5\).

Step2: Plot the y - intercept

The y - intercept is \(b = 5\), so we plot the point \((0,5)\) on the y - axis.

Step3: Use the slope to find another point

The slope \(m=-\frac{3}{4}=\frac{\text{rise}}{\text{run}}\). From the point \((0,5)\), we move down 3 units (because the rise is - 3) and then move 4 units to the right (because the run is 4). This gives us the point \((0 + 4,5-3)=(4,2)\). We can also move up 3 units and left 4 units from \((0,5)\) to get another point \((0 - 4,5 + 3)=(-4,8)\).

Step4: Draw the line

Draw a straight line through the points we have plotted (e.g., \((0,5)\), \((4,2)\), \((-4,8)\)) to graph the line \(y =-\frac{3}{4}x+5\).

Answer:

To graph \(y =-\frac{3}{4}x + 5\):

1. Plot the y - intercept \((0,5)\).
2. Use the slope \(-\frac{3}{4}\) to find additional points (e.g., from \((0,5)\), move down 3, right 4 to get \((4,2)\) or up 3, left 4 to get \((-4,8)\)).
3. Draw a straight line through the plotted points.