To graph the equation \(\( 9x - 6y = 18 \)\) using intercepts, follow these steps:
### Step 1: Find the x-intercept
The x-intercept is where the graph crosses the x-axis, which means \(\( y = 0 \)\).
1. Substitute \(\( y = 0 \)\) into the equation:
\(\[
9x - 6(0) = 18 \implies 9x = 18
\]\)
2. Solve for \(\( x \)\):
\(\[
x = \frac{18}{9} = 2
\]\)
So, the x-intercept is \(\((2, 0)\)\).
### Step 2: Find the y-intercept
The y-intercept is where the graph crosses the y-axis, which means \(\( x = 0 \)\).
1. Substitute \(\( x = 0 \)\) into the equation:
\(\[
9(0) - 6y = 18 \implies -6y = 18
\]\)
2. Solve for \(\( y \)\):
\(\[
y = \frac{18}{-6} = -3
\]\)
So, the y-intercept is \(\((0, -3)\)\).
### Step 3: Plot the intercepts
1. Plot the point \(\((2, 0)\)\) on the x-axis.
2. Plot the point \(\((0, -3)\)\) on the y-axis.
### Step 4: Draw the line
1. Draw a straight line through the two plotted points \(\((2, 0)\)\) and \(\((0, -3)\)\).
This line represents the equation \(\( 9x - 6y = 18 \)\).
### Verifying with Slope-Intercept Form
We can also convert the equation to the slope-intercept form \(\( y = mx + b \)\) to confirm our points and facilitate graphing:
1. Rewrite the original equation \(\( 9x - 6y = 18 \)\) in terms of \(\( y \)\):
\(\[
9x - 6y = 18 \implies -6y = -9x + 18 \implies y = \frac{9x - 18}{6} \implies y = \frac{3}{2}x - 3
\]\)
This confirms the y-intercept \(\((0, -3)\)\) and gives us the slope \(\(\frac{3}{2}\)\), which can be used to verify the line through another method.
### Summary
- The x-intercept is \(\((2, 0)\)\).
- The y-intercept is \(\((0, -3)\)\).
- Plot these points on a graph.
- Draw a line through these points to graph the equation.
Remember to label the axes and provide a title for the graph to clearly illustrate the plotted line.
