Question

the points (-1.6, 2.6) and (2.5, 9.57) are on the graph of a linear relationship between two variables, x and y. What is the constant rate of change of y with respect to x?

Answer 1

To find the Constant rate of change of "y" with respect to "x", you can apply the formula for calculate the slope of a line. This is:

$m=\frac{y_2-y_1}{x_2-x_1}$

You know that this line passes through the points (-1.6, 2.6) and (2.5, 9.57). Then, you can set up the following:

$\begin{gathered} y_2=9.57 \\ y_1=2.6 \\ x_2=2.5 \\ x_1=-1.6 \end{gathered}$

Now you must substitute the corresponding coordinates into the formula for calculate the slope of a line:

$m=\frac{9.57-2.6}{2.5-(-1.6)}$

Evaluating, you get that the constant rate of change of "y" with respect to "x" is:

$\begin{gathered} m=\frac{17}{10} \\ m=1.7 \end{gathered}$