Question

kuta software - infinite algebra 1
finding slope from two points
find the slope of the line through each pair of points.

1. (19, -16), (-7, -15) 2) (1, -19), (-2, -7)
2. (-4, 7), (-6, -4) 4) (20, 8), (9, 16)
3. (17, -13), (17, 8) 6) (19, 3), (20, 3)
4. (3, 0), (-11, -15) 8) (19, -2), (-11, 10)

Explanation:

Problem 1: Find the slope of the line through \((19, -16)\) and \((-7, -15)\)

Step1: Recall the slope formula

The slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Here, \(x_1 = 19\), \(y_1=-16\), \(x_2=-7\), \(y_2 = - 15\).

Step2: Substitute the values into the formula

\(m=\frac{-15-(-16)}{-7 - 19}=\frac{-15 + 16}{-26}=\frac{1}{-26}=-\frac{1}{26}\)

Step1: Use the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\)

Here, \(x_1 = 1\), \(y_1=-19\), \(x_2=-2\), \(y_2=-7\).

Step2: Substitute and calculate

\(m=\frac{-7-(-19)}{-2 - 1}=\frac{-7 + 19}{-3}=\frac{12}{-3}=-4\)

Step1: Apply the slope formula

\(x_1=-4\), \(y_1 = 7\), \(x_2=-6\), \(y_2=-4\), \(m=\frac{y_2 - y_1}{x_2 - x_1}\)

Step2: Compute the slope

\(m=\frac{-4 - 7}{-6-(-4)}=\frac{-11}{-6 + 4}=\frac{-11}{-2}=\frac{11}{2}\)

Answer:

\(-\frac{1}{26}\)

Problem 2: Find the slope of the line through \((1, -19)\) and \((-2, -7)\)