Which equation has the rate of change GREATER THAN the rate of change for the line?

y= 3x-1

y= x/2=4

y=2x+2

y=x/3-3

confusing wording

Anyway, for y = mx + b
m is the slope, or the rate of change

the greater the value of m, the greater the rate of change.

y equal 3x negative 1

Well, well, well, let's see what we have here! The equation that has a rate of change greater than the rate of change for the line y = 3x - 1 is... drumroll please... y = 2x + 2! It's got a little extra oomph in terms of slope, making it speedier than the first equation. So, if you're looking for some fast-paced mathematical action, y = 2x + 2 is the way to go!

To determine which equation has a rate of change greater than the rate of change for the line y=3x-1, we need to compare the slopes of the lines.

The slope of a line is represented by the coefficient of x in its equation.

For the line y=3x-1, the slope is 3.

Let's calculate the slopes for each equation:

1) y = x/2 + 4
The coefficient of x is 1/2, so the slope is 1/2.

2) y = 2x + 2
The coefficient of x is 2, so the slope is 2.

3) y = x/3 - 3
The coefficient of x is 1/3, so the slope is 1/3.

Comparing the slopes, we see that:
- The slope of the first equation (y = x/2 + 4) is less than the slope of y = 3x-1.
- The slope of the second equation (y = 2x + 2) is greater than the slope of y = 3x-1.
- The slope of the third equation (y = x/3 - 3) is less than the slope of y = 3x-1.

Therefore, the equation with a rate of change greater than the rate of change for y=3x-1 is y = 2x + 2.

To determine which equation has a greater rate of change than the line y = 3x - 1, we need to compare the coefficients of x in each equation. The coefficient of x represents the rate of change.

Let's compare the coefficients of x in each equation:

1. y = 3x - 1
The coefficient of x is 3. This means that for every unit increase in x, y increases by 3 units.

2. y = x/2 + 4
The coefficient of x is 1/2. This means that for every unit increase in x, y increases by 1/2 unit.

3. y = 2x + 2
The coefficient of x is 2. This means that for every unit increase in x, y increases by 2 units.

4. y = x/3 - 3
The coefficient of x is 1/3. This means that for every unit increase in x, y increases by 1/3 unit.

Comparing the coefficients, we can see that the equation y = 3x - 1 has the largest coefficient of x, which means it has the greatest rate of change compared to the other equations. Therefore, none of the given equations have a rate of change greater than the rate of change for the line y = 3x - 1.