Compute the slopes for the two given functions and determine which function has a greater rate of change. (i) y = 3x + 5 and (ii) Table function

Question

X|Y
2|5
3|9
4|13
The answer choices are 

A. The function y = 3x +5 has a greater rate of change.
B. The table function has a greater rate of change.
C. The function y = 3x +5 and the table function have an equal rate of change.
D. Both the functions have no rate of change.

Answer 1

Uriah, for this problem you need to know how to identify slope when given an equation as well as a table in order to compare them. Slope is another way to say "rate of change."

 

For the first equation, you have y=3x+5 which is in slope-intercept form. This means that the equation explicitly tells you both the slope and the y-intercept (where it crosses the y-axis). In general, the equation for slope-intercept is y=mx+b with m as the slope and b as the y-intercept. Since m represents a number m in this case is 3 meaning that the rate of change is consistently 3.

 

For the table given, you have both parts of a coordinate for points on a line: (2,5) (3,9) (4,13). The easiest way to find the rate of change is to look for the differences between two points with respect to their coordinate parts. Let's take the first two points and assign them: (2,5) for (x1, y1) and (3,9) for (x2, y2). The rate of change can be found by looking for the difference in y values over the difference in x values.

 

The math would look like this:

m= (y2 -y1)/(x2-x1)

m= (9-5)/(3-2)

m=4/1

m=4

 

Given these two points, the slope or rate of change is 4. This works if you check if (4,13) fits the pattern:

m=(13-9)/(4-3)

m=4/1

m=4

 

Knowing that 4 is greater than 3, the rate of change from the table is greater than that from the equation. Therefore, the answer is choice B.