Rewrite the standard equation in slope-intercept form: 3x – 8y = 24
The Correct Answer and Explanation is:
To rewrite the equation 3x−8y=243x – 8y = 243x−8y=24 in slope-intercept form, we aim to solve for yyy and express the equation in the form y=mx+by = mx + by=mx+b, where mmm is the slope and bbb is the y-intercept.
Step 1: Isolate the yyy-term
We start with the equation:3x−8y=243x – 8y = 243x−8y=24
The goal is to isolate yyy, so first subtract 3x3x3x from both sides:−8y=−3x+24-8y = -3x + 24−8y=−3x+24
Step 2: Solve for yyy
Now, divide both sides of the equation by −8-8−8 to solve for yyy:y=−3x+24−8y = \frac{-3x + 24}{-8}y=−8−3x+24
Step 3: Simplify the equation
We can simplify each term in the numerator by dividing by −8-8−8:y=−3x−8+24−8y = \frac{-3x}{-8} + \frac{24}{-8}y=−8−3x+−824
This simplifies to:y=38x−3y = \frac{3}{8}x – 3y=83x−3
Step 4: Final result
Thus, the equation in slope-intercept form is:y=38x−3y = \frac{3}{8}x – 3y=83x−3
Explanation:
In slope-intercept form, y=mx+by = mx + by=mx+b, the term mmm represents the slope of the line, and bbb represents the y-intercept, where the line crosses the y-axis. From our final equation:
- The slope m=38m = \frac{3}{8}m=83, meaning that for every 8 units the line moves horizontally (along the x-axis), it moves 3 units vertically (along the y-axis).
- The y-intercept b=−3b = -3b=−3, which means the line crosses the y-axis at (0,−3)(0, -3)(0,−3).
This form is useful because it makes it easy to graph the line or identify key features like the slope and y-intercept.
