Rewrite in slope-intercept form: 6x + 2y = 12
A. y = -3x + 6
B. y = 3x +12
C. y = 3x – 6
D. y = 6x – 12
E. None
The Correct Answer and Explanation is :
To rewrite the equation (6x + 2y = 12) in slope-intercept form, we need to solve for (y).
Step-by-Step Process:
- Start with the given equation:
[
6x + 2y = 12
] - Isolate the (y)-term:
Subtract (6x) from both sides to move the (x)-term to the right-hand side:
[
2y = -6x + 12
] - Solve for (y):
Divide both sides of the equation by 2 to get (y) by itself:
[
y = \frac{-6x + 12}{2}
]
Simplify the terms:
[
y = -3x + 6
]
Thus, the equation in slope-intercept form is:
[
y = -3x + 6
]
Slope-Intercept Form:
The slope-intercept form of an equation is written as (y = mx + b), where:
- (m) is the slope of the line.
- (b) is the y-intercept, the point where the line crosses the y-axis.
In the equation (y = -3x + 6):
- The slope (m = -3), meaning that for every unit increase in (x), (y) decreases by 3 units.
- The y-intercept (b = 6), meaning the line crosses the y-axis at (y = 6).
Answer:
The correct answer is:
A. y = -3x + 6
I will now generate an image to visually show the slope-intercept form equation.
Here is the graph that represents the equation (y = -3x + 6). It shows how the line behaves, crossing the y-axis at 6 and having a slope of -3. This visual should help you understand the relationship between the equation and the graph! Let me know if you need further explanation or another visual.
