: 3X 8y -24 Click to select points on the graph: h0′
The Correct Answer and Explanation is:
To graph the equation 3x+8y=243x + 8y = 243x+8y=24 using intercepts, we will find the x-intercept and y-intercept.
Step 1: Find the x-intercept.
The x-intercept occurs when y=0y = 0y=0. Substitute y=0y = 0y=0 into the equation:3x+8(0)=243x + 8(0) = 243x+8(0)=243x=243x = 243x=24x=243=8x = \frac{24}{3} = 8x=324=8
So, the x-intercept is (8,0)(8, 0)(8,0).
Step 2: Find the y-intercept.
The y-intercept occurs when x=0x = 0x=0. Substitute x=0x = 0x=0 into the equation:3(0)+8y=243(0) + 8y = 243(0)+8y=248y=248y = 248y=24y=248=3y = \frac{24}{8} = 3y=824=3
So, the y-intercept is (0,3)(0, 3)(0,3).
Step 3: Plotting the intercepts.
Now that we have the intercepts:
- x-intercept: (8,0)(8, 0)(8,0)
- y-intercept: (0,3)(0, 3)(0,3)
You can plot these two points on the graph:
- The point (8,0)(8, 0)(8,0) on the x-axis.
- The point (0,3)(0, 3)(0,3) on the y-axis.
Step 4: Draw the line.
Now, draw a straight line through these two points. This line represents the equation 3x+8y=243x + 8y = 243x+8y=24.
Conclusion:
- The equation 3x+8y=243x + 8y = 243x+8y=24 is a straight line.
- It intersects the x-axis at (8,0)(8, 0)(8,0) and the y-axis at (0,3)(0, 3)(0,3).
- The graph of the line passes through these two points, and you can use these intercepts to sketch the function.
