Exercise 37 Page 299

We want to use the Slope Formula to find the slope of the line that passes through the given points. m = y_2-y_1/x_2-x_1 In the above formula, m represents the slope, and (x_1,y_1) and (x_2,y_2) two points on the line.

Calculating the Slope

In this exercise, we are given the points (- 42.25,5.2) and (3.25,3). Note that when substituting these values into the Slope Formula, it does not matter which point we choose to use as ( x_1, y_1) or ( x_2, y_2). m=3- 5.2/3.25-( - 42.25) or m=5.2- 3/- 42.25- 3.25 Both will give the same result. Here, we will use the points in the given order and solve for the slope m.

The slope that passes through the given points is approximately - 0.048352. This means that as x increases, y decreases.

Check by Graphing

Finally, let's plot the given points and connect them with a line to check if the direction of the slope matches what we calculated above.

Observing the graph, we can confirm that as x moves in the positive direction, y moves in the negative direction.