Compare Linear Function 1 with Linear Function 2. Which one has the greater rate of change?

Question

Linear function 1: y = 15x + 8

Linear function 2:

x y
5 26
13 34

Answer 1

To compare the rate of change of Linear Function 1 with Linear Function 2, we first need to identify the slope (rate of change) for each function.

Linear Function 1:

The equation is given as: $$y=15x+8$$ In this equation, the coefficient of $x$ (which is 15) represents the slope. Therefore, the rate of change for Linear Function 1 is 15.

Linear Function 2:

For Linear Function 2, we can determine the slope using the two points provided: (5, 26) and (13, 34).

The formula for the slope $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is: $$m=\frac{y_2-y_1}{x_2-x_1}$$

Substituting the points into the formula:

• Let $(x_1,y_1)=(5,26)$
• Let $(x_2,y_2)=(13,34)$

Now calculate the slope: $$m=\frac{34-26}{13-5}=\frac{8}{8}=1$$

Summary of Rates of Change:

• Linear Function 1 has a rate of change (slope) of 15.
• Linear Function 2 has a rate of change (slope) of 1.

Conclusion:

Linear Function 1 has a greater rate of change than Linear Function 2, as 15 is greater than 1.

Answer 2

you sure

Answer 3

Yes, let's go over the calculations again step by step to ensure accuracy.

Linear Function 1:

The equation is given as: $$y=15x+8$$

In this equation:

• The slope (rate of change) is the coefficient of $x$, which is 15.

Linear Function 2:

The points provided are:

• Point 1: (5, 26)
• Point 2: (13, 34)

To find the slope (rate of change), we'll use the slope formula: $$m=\frac{y_2-y_1}{x_2-x_1}$$

Substituting the values:

• $y_1=26$, $y_2=34$
• $x_1=5$, $x_2=13$

Now plug in the values: $$m=\frac{34-26}{13-5}=\frac{8}{8}=1$$

Summary:

• Linear Function 1 has a slope of 15.
• Linear Function 2 has a slope of 1.

Conclusion:

Linear Function 1 does indeed have a greater rate of change (slope of 15) compared to Linear Function 2 (slope of 1). I confirm that the comparison is accurate. Thank you for your patience!