Question

Below you are given two points on a graph and a line connecting them. Use the slope triangle to determine the point-slope form of the line. What is m?

a) m = 0
b) m = 1
c) m = 2
d) m = -2

Answer 1

To calculate the slope (m) for the line passing through Point 1: (1, 0.1) and Point 2: (7, 26.8), we find the rise over run which gives us a slope value of approximately 4.45. Therefore, the correct answer is b. 4.5.

Step-by-step explanation:

To find the slope, or m, of a line passing through two points, we use the formula for slope which is (change in y) / (change in x). This is also known as the rise over run. Given Point 1 at (1, 0.1) and Point 2 at (7, 26.8), we can calculate the slope by subtracting the y-value of Point 1 from the y-value of Point 2 and then dividing by the subtraction of the x-value of Point 1 from the x-value of Point 2.

Using the given points, the calculation for the slope would be as follows:

1. Change in y = y2 - y1 = 26.8 - 0.1 = 26.7
2. Change in x = x2 - x1 = 7 - 1 = 6
3. Slope (m) = (Change in y) / (Change in x) = 26.7 / 6 ≈ 4.45

The correct answer is b. 4.5.

The m term in an equation for a straight line like y = mx + b represents the slope of the line. As a general rule, when determining the slope using two points, it's advisable to select points that are widely separated on the line to minimize potential errors.