Graph both equations and conpare the rate of change in both graphs.
1: y = 2x + 1
2: y = 1/4x - 2
I've already graphed them correctly, but comparing the rate of change confuses me. ( Doing summer HM ) I did 2 x 1/4 and got 8. Is this correct?
rates of change is the slope of the line
the slope of the first line is 2
the slope of the second line is 1/4
The larger the slope, the greater the rate of change, so what do you think?
To compare the rate of change between two graphs, you need to determine the slope of each equation since the slope represents the rate of change.
The slope of an equation in the form y = mx + b, where m is the slope, can be extracted from the coefficient of x.
In the first equation, y = 2x + 1, the coefficient of x is 2. Therefore, the slope is 2.
In the second equation, y = 1/4x - 2, the coefficient of x is 1/4. Therefore, the slope is 1/4.
Now that we have the slopes, we can compare them. When comparing slopes, we consider their magnitude. A larger slope represents a steeper line, indicating a higher rate of change. A smaller slope represents a shallower line, indicating a lower rate of change.
Comparing the slopes we found:
Slope of the first equation (y = 2x + 1): 2
Slope of the second equation (y = 1/4x - 2): 1/4
Since 2 is greater than 1/4, we can conclude that the rate of change (or slope) of the first equation is greater than the rate of change (or slope) of the second equation.
Regarding your calculation, when you multiplied 2 by 1/4, you obtained 8. However, it seems like a mistake. To compare the slopes, we don't perform any multiplication of the slopes themselves. Instead, we compare the magnitudes of the slopes directly.