12x + 2y = -12 in slope intercept form
The Correct Answer and Explanation is:
To rewrite the equation 12x+2y=−1212x + 2y = -1212x+2y=−12 in slope-intercept form (y=mx+by = mx + by=mx+b), we need to solve for yyy. Here’s the step-by-step process:
Step 1: Start with the original equation
12x+2y=−1212x + 2y = -1212x+2y=−12
Step 2: Isolate the yyy-term
To isolate the yyy-term, subtract 12x12x12x from both sides of the equation:
2y=−12−12x2y = -12 – 12x2y=−12−12x
Now the equation looks like:
2y=−12−12x2y = -12 – 12x2y=−12−12x
Step 3: Solve for yyy
Next, divide every term by 2 to solve for yyy:
y=−12−12x2y = \frac{-12 – 12x}{2}y=2−12−12x
This simplifies to:
y=−6−6xy = -6 – 6xy=−6−6x
Step 4: Write the equation in slope-intercept form
Now the equation is in slope-intercept form:
y=−6−6xy = -6 – 6xy=−6−6x
This is the slope-intercept form of the equation, where:
- The slope (mmm) is −6-6−6, indicating that for every 1 unit increase in xxx, yyy decreases by 6 units.
- The y-intercept (bbb) is −6-6−6, meaning the line crosses the y-axis at y=−6y = -6y=−6.
Explanation:
Slope-intercept form is a way to express a linear equation where the equation is written as y=mx+by = mx + by=mx+b. Here, mmm is the slope of the line, and bbb is the y-intercept. By solving the equation 12x+2y=−1212x + 2y = -1212x+2y=−12 for yyy, we were able to rewrite it in the desired form, making it easier to understand how the line behaves. The slope of −6-6−6 shows the steepness and direction of the line, and the intercept of −6-6−6 gives us the point where the line crosses the y-axis.
