Question

For each pair of points, find the slope of the line that passes through both points. If you get stuck, try plotting the points on graph paper and drawing the line through them with a ruler. 1. (1,1) and (7,5) 2. (1,1) and (5,7) 3. (2,5) and (-1,2) 4. (2,5) and (-7,-4)

Answer 1

To find the slopes of the line that passes through the points (1, 1) and (7, 5), we can follow the next steps:

1. Identify the coordinates of the points:

x1 = 1

y1 = 1

x2 = 7

y2 = 5

2. Apply the formula of the slope of a line:

$m=\frac{y_2-y_1}{x_2-x_1}\Rightarrow m=\frac{5-1}{7-1}\Rightarrow m=\frac{4}{6}\Rightarrow m=\frac{2}{3}$

Then, the slope of the line that passes through the points (1, 1) and (7, 5) is m = 2/3.

2. We can follow the same for case 2. (1, 1) and (5, 7):

x1 = 1

y1 = 1

x2 = 5

y2 = 7

Then

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{7-1}{5-1}\Rightarrow m=\frac{6}{4}\Rightarrow m=\frac{3}{2}$

Then, the slope of the line that passes through the points (1, 1) and (5, 7) is m = 3/2.

3. We can follow the same for case 3, (2, 5) and (-1, 2):

x1 = 2

y1 = 5

x2 = -1

y2 = 2

$m=\frac{2-5}{-1-2}\Rightarrow m=\frac{-3}{-3}\Rightarrow m=1$

Then, the slope of the line that passes through the points (2, 5) and (-1, 2) is m = 1.

4. We can follow the same for case 4, (2,5) and (-7, -4):

x1 = 2

y1 = 5

x2 = -7

y2 = -4

$m=\frac{-4-5}{-7-2}\Rightarrow m=\frac{-9}{-9}\Rightarrow m=1$

Then, the slope of the line that passes through the points (2, 5) and (-7, -4) is m = 1.