Which function has greater rate of change?
y = 3x – 7
2x + y = 7
(y – 3) = 4(x – 1)
5x – 10y = 2
To determine which function has a greater rate of change, we can compare the slopes of the linear equations. The slope of a linear equation in the form y = mx + b is equal to m.
1) y = 3x – 7
The slope of this equation is 3.
2) 2x + y = 7
Rearranging the equation to slope-intercept form, we have y = -2x + 7.
The slope of this equation is -2.
3) (y – 3) = 4(x – 1)
Expanding the equation, we have y - 3 = 4x - 4.
Rearranging the equation to slope-intercept form, we have y = 4x - 1.
The slope of this equation is 4.
4) 5x – 10y = 2
Dividing the equation by -10, we have y = -0.5x - 0.2.
The slope of this equation is -0.5.
From the comparison of slopes:
3 > -2 > 4 > -0.5
Therefore, the function with the greatest rate of change is y = 3x - 7.
To determine which function has a greater rate of change, we need to compare the coefficients of the variables that change. In this case, we will compare the coefficients of x and y in each equation.
1. y = 3x – 7:
- The coefficient of x is 3.
- The coefficient of y is 0 (since it is not explicitly stated).
2. 2x + y = 7:
- The coefficient of x is 2.
- The coefficient of y is 1.
3. (y – 3) = 4(x – 1):
- The coefficient of x is 4.
- The coefficient of y is 1.
4. 5x – 10y = 2:
- The coefficient of x is 5.
- The coefficient of y is -10.
Comparing the coefficients, we can see that the function with the greatest rate of change is the one with the largest coefficient for x. In this case, it is equation 4: 5x – 10y = 2.