Question

Finding Slope and Graphing Equations of Lines Part 1 Directions: find the slope of the line passing through the given points. Then tell whether the line rises, falls, is horizontal, or is vertical. Show all work. 1.) (8, 15) and (12, -1) 2.) (5,-2) and (2,-2) 3.) (9, -3) and (-6,4) 4.) (4, 5) and (21,5)

Answer 1

The slope of a line is given by

$m=\frac{y_2−y_1}{ x_2−x_1}$

1: (8, 15) and (12, -1)

$(x_1,y_1)=(8,15)\text{ and }(x_2,y_2)=(12,-1)$

So the slope is

$m=\frac{-1-15}{12-8}=\frac{-16}{4}=-4$

Since the slope is negative, the line falls.

2: (5,-2) and (2,-2)

$(x_1,y_1)=(5,-2)\text{ and }(x_2,y_2)=(2,-2)$

So the slope is

$m=\frac{-2-(-2)}{2-5}=\frac{-2+2}{-3}=\frac{0}{3}=0$

Since the slope is 0, the line is a flat horizontal line.

3: (9, -3) and (-6,4)

$(x_1,y_1)=(9,-3)\text{ and }(x_2,y_2)=(-6,4)$

So the slope is

$m=\frac{4-(-3)}{-6-9}=\frac{4+3}{-15}=-\frac{7}{15}$

Since the slope is negative, the line falls.

4: (4, 5) and (21, 5)​

$(x_1,y_1)=(4,5)\text{ and }(x_2,y_2)=(21,5)$$m=\frac{5-5}{21-4}=\frac{0}{17}=0$

Since the slope is 0, the line is a flat horizontal line.