-2x+6 what is the rate of change between the two variables, what is the y intercept, can you Also answer these same questions for the equation y = -3x + 10
rate of change is how fast y changes when x changes by 1.
y = -2x+6
Note that -2 in front of x. That is the slope of the line, or also the rate of change. You can see that adding 1 to x add -2 to y. So, -2 is the rate of change (of y with respect to x).
y = -3x+10
slope = -3
You have to have y all by itself to read off the slope from the equation.
3y = 9x+12
y = 3x+4
slope = 3
To determine the rate of change and the y-intercept for the equation -2x + 6, we can compare it to the standard slope-intercept form, y = mx + b, where m represents the slope (rate of change) and b represents the y-intercept.
Comparing -2x + 6 to y = mx + b, we can determine the values as follows:
1. Rate of Change (slope):
In this case, the coefficient of x is -2. Thus, the rate of change (slope) is -2.
2. Y-intercept:
The constant term (the term without x) is 6. Therefore, the y-intercept is 6.
Now, let's do the same for the equation y = -3x + 10:
1. Rate of Change (slope):
In this case, the coefficient of x is -3. Hence, the rate of change (slope) is -3.
2. Y-intercept:
The constant term (the term without x) is 10. So, the y-intercept for this equation is 10.
To summarize:
For the equation -2x + 6:
- Rate of change (slope) = -2
- Y-intercept = 6
For the equation y = -3x + 10:
- Rate of change (slope) = -3
- Y-intercept = 10
To find the rate of change and the y-intercept of a linear equation, such as -2x+6 and y = -3x + 10, we can compare them to the standard form of a linear equation, which is y = mx + b.
First, let's identify the rate of change, also known as the slope (m). In the equation -2x + 6, the coefficient of x is -2. Therefore, the rate of change is -2. In y = -3x + 10, the coefficient of x is -3. Hence, the rate of change is -3.
The y-intercept (b) represents the point where the line crosses the y-axis. In -2x+6, the constant term is 6, which means the line intersects the y-axis at the point (0, 6). Therefore, the y-intercept is 6. In y = -3x + 10, the constant term is 10, indicating that the line passes through the point (0, 10). Therefore, the y-intercept is 10.
To summarize:
- For -2x + 6:
- Rate of change: -2
- Y-intercept: 6
- For y = -3x + 10:
- Rate of change: -3
- Y-intercept: 10
Remember, the rate of change is the change in y divided by the change in x, and the y-intercept is the point where the line intersects the y-axis.