Question

1. draw a line through the given coordinates and identify the types of slopes.

a. (5, 1) and (2, 4)
b. (-2, 3) and (-2, -5)
c. (-1, 2) and (-4, 0)

Explanation:

Step1: Recall slope - formula

The slope formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).

Step2: Calculate slope for part a

For points \((5,1)\) and \((2,4)\), let \((x_1,y_1)=(5,1)\) and \((x_2,y_2)=(2,4)\). Then \(m=\frac{4 - 1}{2 - 5}=\frac{3}{-3}=- 1\).

Step3: Calculate slope for part b

For points \((-2,3)\) and \((-2,-5)\), let \((x_1,y_1)=(-2,3)\) and \((x_2,y_2)=(-2,-5)\). Then \(m=\frac{-5 - 3}{-2-(-2)}=\frac{-8}{0}\), which is undefined (vertical line).

Step4: Calculate slope for part c

For points \((-1,2)\) and \((-4,0)\), let \((x_1,y_1)=(-1,2)\) and \((x_2,y_2)=(-4,0)\). Then \(m=\frac{0 - 2}{-4-(-1)}=\frac{-2}{-3}=\frac{2}{3}\).

Answer:

a. The slope is - 1.
b. The slope is undefined.
c. The slope is \(\frac{2}{3}\).