Question

graph the equation below.
3x + 9y = 9
show your work here

Explanation:

Step1: Rewrite in slope - intercept form

We want to rewrite the equation \(3x + 9y=9\) in the form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.
First, isolate \(y\):
Subtract \(3x\) from both sides: \(9y=-3x + 9\)
Then divide each term by 9: \(y=-\frac{3}{9}x+\frac{9}{9}\), which simplifies to \(y =-\frac{1}{3}x + 1\)

Step2: Find the y - intercept

The y - intercept \(b = 1\). So when \(x = 0\), \(y=1\). This gives us the point \((0,1)\)

Step3: Find another point using the slope

The slope \(m=-\frac{1}{3}\), which means for every 3 units we move to the right (increase \(x\) by 3), we move down 1 unit (decrease \(y\) by 1).
Starting from the y - intercept \((0,1)\), if we let \(x = 3\), then \(y=-\frac{1}{3}(3)+1=- 1 + 1=0\). So we get the point \((3,0)\)

Step4: Graph the line

Plot the points \((0,1)\) and \((3,0)\) (and any other points you find using the slope - intercept form) and draw a straight line through them.

Answer:

To graph \(3x + 9y = 9\) (or \(y=-\frac{1}{3}x + 1\)):

1. Plot the y - intercept \((0,1)\) (since when \(x = 0\), \(y = 1\)).
2. Use the slope \(m=-\frac{1}{3}\) to find another point. From \((0,1)\), move 3 units right to \(x = 3\) and 1 unit down to \(y=0\), giving the point \((3,0)\).
3. Draw a straight line through the points \((0,1)\) and \((3,0)\) (and extend it in both directions).