Question

geometry
© 2016 kuta software llc. all r
parallel and perpendicular slopes h
find the slope of the line through each pair of

1. (19, -1), (19, -19)
2. (20, 12), (-16, -20)

find the slope that is parallel to the pair of

1. (4, -2), (16, 0)
2. (20, 7), (8, 0)

Explanation:

Step1: Recall the slope formula

The slope formula is \(m = \frac{y_2 - y_1}{x_2 - x_1}\), where \((x_1,y_1)\) and \((x_2,y_2)\) are two points on the line.

Step2: Calculate the slope for \((19,-1),(19,-19)\)

Here \(x_1 = 19,y_1=-1,x_2 = 19,y_2=-19\). Substitute into the formula: \(m=\frac{-19 - (-1)}{19 - 19}=\frac{-18}{0}\). Division by zero is undefined.

Step3: Calculate the slope for \((20,12),(-16,-20)\)

Here \(x_1 = 20,y_1 = 12,x_2=-16,y_2=-20\). Substitute into the formula: \(m=\frac{-20 - 12}{-16 - 20}=\frac{-32}{-36}=\frac{8}{9}\).

Step4: Calculate the slope for \((4,-2),(16,0)\)

Here \(x_1 = 4,y_1=-2,x_2 = 16,y_2 = 0\). Substitute into the formula: \(m=\frac{0 - (-2)}{16 - 4}=\frac{2}{12}=\frac{1}{6}\). Since parallel lines have the same slope, the slope of a line parallel to the line through \((4,-2),(16,0)\) is \(\frac{1}{6}\).

Step5: Calculate the slope for \((20,7),(8,0)\)

Here \(x_1 = 20,y_1 = 7,x_2 = 8,y_2 = 0\). Substitute into the formula: \(m=\frac{0 - 7}{8 - 20}=\frac{-7}{-12}=\frac{7}{12}\). Since parallel lines have the same slope, the slope of a line parallel to the line through \((20,7),(8,0)\) is \(\frac{7}{12}\).

Answer:

1. Undefined; 3) \(\frac{8}{9}\); 5) \(\frac{1}{6}\); 7) \(\frac{7}{12}\)