180 Easy Algebra Step-by-Step
Solution
a. (−1, 4) and (5, −3)Step 1. Specify (x 1 , y 1 ) and (x 2 , y 2 ) and identify values for x 1 , y 1 , x 2 , and y 2.
Let (x 1 , y 1 ) = (−1, 4) and (x 2 , y 2 ) = (5, −3). Then x 1 = −1, y 1 = 4, x 2 = 5,
and y 2 = −3.Step 2. Evaluate the formula for the values from step 1.m =yy
xxy 1
21 x=
()−
()
)− 4
5 −(−
=
− 34 −
51 +
=
− 7
6
= −
7
6
Step 3. State the slope.
The slope of the line through (−1, 4) and (5, −3) is −7
6
. Note: If you
sketch the line through these two points, you will see that it slants
downward from left to right—so its slope should be negative.
b. (−6, 7) and (5, 7)
Step 1. Specify (x 1 , y 1 ) and (x 2 , y 2 ) and identify values for x 1 , y 1 , x 2 , and y 2.
Let (x 1 , y 1 ) = (−6, 7) and (x 2 , y 2 ) = (5, 7). Then x 1 = −6, y 1 = 7, x 2 = 5,
and y 2 = 7.Step 2. Evaluate the formula for the values from step 1.m =yy
xxy 1
21 x=
77
5 () 6
=
77
56
=
0
11
= 0
Step 3. State the slope.
The slope of the line that contains (−6, 7) and (5, 7) is 0. Note: If you
sketch the line through these two points, you will see that it is a hor-
izontal line—so the slope should be 0.c. (5, 8) and (5, −3)
Step 1. Specify (x 1 , y 1 ) and (x 2 , y 2 ) and identify values for x 1 , y 1 , x 2 , and y 2.
Let (x 1 , y 1 ) = (5, 8) and (x 2 , y 2 ) = (5, −3). Then x 1 = 5, y 1 = 8, x 2 = 5, and
y 2 = −3.Step 2. Evaluate the formula for the values from step 1.m=yy
xxy 1
21 x=
()− )− 8
55 −
=
− 38 −
55 −
=
− 11
0
= undefi ned