Question

Given the function f(x) = 4x + 10 and g(x), which function has a greater slope? x g(x) 2 5 4 7 6 9

Answer 1

The slope of g(x) is found to be 1 using two provided points. The function f(x) = 4x + 10 has a constant slope of 4. Hence, f(x) has a greater slope than g(x).

Step-by-step explanation:

To determine which function has the greater slope, we first have to find the slope of the function g(x). We can use the coordinate pairs given for g(x) to calculate the slope. The slope is the change in y divided by the change in x, often referred to as 'rise over run'. Using the points (2, 5) and (4, 7), the slope can be calculated as:

Slope of g(x) = (7 - 5) / (4 - 2) = 2 / 2 = 1

The function f(x) = 4x + 10 has a constant slope of 4 since it is a linear function in the form y = mx + b, where m is the slope. Therefore, f(x) has a greater slope than g(x).

Answer 2

Function f(x) has slope 4, which is greater.

Step-by-step explanation:

Next time please present your data in tabular form:

x g(x)

2 5

4 7

6 9

From this table it is immediately evident that if x increases by 2, y increases by 2 also. Thus, the slope of the line is m = rise / run = 2 / 2 = 1, for function g(x). Function f(x) has slope 4, which is greater.