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The given equation is \( 8x + 6y = 24 \). To graph this, we can rearrange it into the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

### Step-by-Step Process:

1. **Convert to slope-intercept form**:
   \[
   8x + 6y = 24
   \]
   Solve for \( y \):
   \[
   6y = -8x + 24
   \]
   \[
   y = \frac{-8}{6}x + \frac{24}{6}
   \]
   Simplify:
   \[
   y = -\frac{4}{3}x + 4
   \]
   Now, the equation is in slope-intercept form, where the slope \( m = -\frac{4}{3} \) and the y-intercept \( b = 4 \).

2. **Find the intercepts**:
   - **Y-intercept**: Set \( x = 0 \), then \( y = 4 \). So, one point is \( (0, 4) \).
   - **X-intercept**: Set \( y = 0 \), solving for \( x \):
     \[
     8x + 6(0) = 24 \quad \Rightarrow \quad 8x = 24 \quad \Rightarrow \quad x = 3
     \]
     So, another point is \( (3, 0) \).

3. **Plot the points**: 
   - Plot \( (0, 4) \) (y-intercept) and \( (3, 0) \) (x-intercept) on the graph.
   - Since the slope is \( -\frac{4}{3} \), the line will slant downwards as you move from left to right.

4. **Draw the line**: Use the points \( (0, 4) \) and \( (3, 0) \) to draw the line on the provided grid.

Would you like more details or have any questions about this process?

### Related Questions:
1. How do you calculate the slope of a line given two points?
2. What is the significance of the y-intercept in a linear equation?
3. How do you find the x-intercept of a line given its equation?
4. What are parallel lines, and how can you identify them by their equations?
5. How do changes in the slope value affect the angle of a line?

### Tip:
To check if a point lies on a line, substitute the coordinates of the point into the equation and see if both sides are equal.

Graph the equation 8x + 6y = 24 on a coordinate plane.

Learn how to graph the linear equation 8x + 6y = 24 step-by-step by converting it to slope-intercept form, finding intercepts, and plotting the line on a coordinate plane. Suitable for Grades 8-10.

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