Question

graph this line using the slope and y-intercept:
$y = -\frac{3}{4}x + 6$
click to select points on the graph.

Explanation:

Step1: Identify y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(b\) is the y - intercept. For \(y=-\frac{3}{4}x + 6\), \(b = 6\). So the y - intercept is the point \((0,6)\).

Step2: Use slope to find next point

The slope \(m=-\frac{3}{4}\). The slope is \(\frac{\text{rise}}{\text{run}}\), so from the point \((0,6)\), we move down 3 units (because the rise is - 3) and then move right 4 units (because the run is 4). So we get the point \((0 + 4,6-3)=(4,3)\). We can also move up 3 units and left 4 units from \((0,6)\) to get \((0 - 4,6 + 3)=(-4,9)\) (but since the graph shows positive x and y values up to 10, \((4,3)\) and \((0,6)\) are easy to plot).

Step3: Draw the line

Plot the points \((0,6)\) and \((4,3)\) (or other points found using the slope) and then draw a straight line through them.

Answer:

To graph the line \(y =-\frac{3}{4}x + 6\):

1. Plot the y - intercept \((0,6)\) (since when \(x = 0\), \(y=6\)).
2. Use the slope \(m=-\frac{3}{4}\): from \((0,6)\), move down 3 units and right 4 units to get the point \((4,3)\) (or up 3 units and left 4 units to get \((- 4,9)\)).
3. Draw a straight line through the plotted points. The key points to plot are \((0,6)\) and \((4,3)\) (among others).