Question

question 2 of 5
use the drawing tools to form the correct answer on the provided graph.
graph the line that represents the equation 3y = 2x + 9

Explanation:

Step1: Rewrite in slope - intercept form

The given equation is \(3y = 2x+9\). We want to write it in the form \(y = mx + b\) (slope - intercept form), where \(m\) is the slope and \(b\) is the y - intercept.
Divide both sides of the equation \(3y=2x + 9\) by 3:
\(y=\frac{2}{3}x + 3\)

Step2: Identify y - intercept and slope

• The y - intercept \(b = 3\). This means the line crosses the y - axis at the point \((0,3)\).
• The slope \(m=\frac{2}{3}\). The slope is the rise over run, so from the y - intercept \((0,3)\), we can go up 2 units and then right 3 units to get another point on the line. For example, from \((0,3)\), moving up 2 (increase in y) and right 3 (increase in x) gives us the point \((3,3 + 2)=(3,5)\). We can also go down 2 units and left 3 units from the y - intercept: from \((0,3)\), moving down 2 (decrease in y) and left 3 (decrease in x) gives us the point \((- 3,3-2)=(-3,1)\).

Step3: Plot the line

Using the two points we found, \((0,3)\) (the y - intercept) and another point like \((3,5)\) or \((-3,1)\), we can draw a straight line passing through these points on the given coordinate grid.

Answer:

To graph the line \(3y = 2x+9\) (or \(y=\frac{2}{3}x + 3\)):

1. Plot the y - intercept at \((0,3)\) (where the line crosses the y - axis).
2. Use the slope \(\frac{2}{3}\) to find another point: from \((0,3)\), move up 2 units and right 3 units to get \((3,5)\) (or down 2 units and left 3 units to get \((-3,1)\)).
3. Draw a straight line through the plotted points.