Write 4x + 3y = 6 in the form y = mx + b.
The Correct Answer and Explanation is:
To rewrite the equation 4x+3y=64x + 3y = 64x+3y=6 in the form y=mx+by = mx + by=mx+b, which is the slope-intercept form of a linear equation, we need to isolate yyy on one side of the equation.
Here are the steps to do that:
- Start with the given equation: 4x+3y=64x + 3y = 64x+3y=6
- Subtract 4x4x4x from both sides to get rid of the 4x4x4x term on the left: 3y=−4x+63y = -4x + 63y=−4x+6
- Now, to isolate yyy, divide both sides of the equation by 3: y=−4x+63y = \frac{-4x + 6}{3}y=3−4x+6
- Simplify the right side by dividing both terms: y=−43x+2y = -\frac{4}{3}x + 2y=−34x+2
So the equation in the slope-intercept form is: y=−43x+2y = -\frac{4}{3}x + 2y=−34x+2
Explanation:
The equation y=mx+by = mx + by=mx+b is called the slope-intercept form of a linear equation. In this form:
- mmm represents the slope of the line.
- bbb represents the y-intercept, which is the point where the line crosses the y-axis.
In the equation y=−43x+2y = -\frac{4}{3}x + 2y=−34x+2:
- The slope m=−43m = -\frac{4}{3}m=−34, which tells you that for every 3 units you move horizontally to the right along the x-axis, the line moves down 4 units. This gives the line a negative slope, meaning it goes downhill from left to right.
- The y-intercept b=2b = 2b=2, meaning the line crosses the y-axis at the point (0, 2).
This process is a common way of rearranging a linear equation to better understand the relationship between the variables and visualize it on a graph.
