Question

Simone claims that the slope of the line through (-2,7) and (3,0) is the same as the slope of the line through (2,1) and (12,-13). Prove or disprove Simone's claim.​

Answer 1

After calculating the slopes for both sets of points, it is determined that Simone's claim is true; both lines have a slope of -1.4.

Step-by-step explanation:

To determine if Simone's claim is true, we need to calculate the slope of both lines using the coordinates given and compare them. The slope is defined as the change in y divided by the change in x (rise over run). We'll calculate the slope for each pair of points.

For the first line passing through points (-2,7) and (3,0), the slope (m) is calculated as:

m = (y2 - y1) / (x2 - x1) = (0 - 7) / (3 - (-2)) = -7 / 5 = -1.4

For the second line passing through points (2,1) and (12,-13), the slope (m) is calculated as:

m = (y2 - y1) / (x2 - x1) = (-13 - 1) / (12 - 2) = -14 / 10 = -1.4

Since both slopes are equal to -1.4, Simone's claim is proven to be true. The slope of the line through the two sets of points is indeed the same.