Question

finding slope guided notes & practice
practice #3
using this method, find the slopes from the tables below:
1.

x	y
1	10
2	15
3	20
4	25
5	30

$(x_1,y_1)=(0,5)$
$(x_2,y_2)=(1,10)$
$m=\frac{10-5}{1-0}=5$
slope$=5$
2.

x	y
-4	4
-6	-2
-8	-8
-10	-14
-12	-20

$(x_1,y_1)=(-2,10)$
$(x_2,y_2)=(-4,4)$
$m=\frac{4-10}{-4-(-2)}=3$
slope$=3$
3.

x	y
3	-2
5	1
7	4
9	7
11	10

$(x_1,y_1)=(1,-5)$
$(x_2,y_2)=(3,-2)$
$m=\frac{-2-(-5)}{3-1}=\frac{3}{2}$
slope$=\frac{3}{2}$
4.

x	y
-2	-4
-1	-7
0	-10
1	-13
2	-16

$(x_1,y_1)=(-3,-1)$
$(x_2,y_2)=(-2,-4)$
$m=\frac{-4-(-1)}{-2-(-3)}=3$
slope$=3$
5.

x	y
0	-2
-3	2
-6	6
-9	10
-12	14

$(x_1,y_1)=(3,-6)$
$(x_2,y_2)=(0,-2)$
$m=\frac{-2-(-6)}{0-3}=-\frac{4}{3}$
slope$=-\frac{4}{3}$
6.

x	y
4	-2
8	-1
12	0
16	1
20	2

$(x_1,y_1)=(0,-3)$
$(x_2,y_2)=(4,-2)$
$m=\frac{-2-(-3)}{4-0}=\frac{1}{4}$
slope$=\frac{1}{4}$
which type of method do you prefer when finding slope?

Explanation:

Step1: Recall slope formula

Slope $m = \frac{y_2 - y_1}{x_2 - x_1}$ for points $(x_1,y_1),(x_2,y_2)$

Step2: Calculate slope for Table1

Pick $(0,5)$ and $(1,10)$:
$m = \frac{10 - 5}{1 - 0} = 5$

Step3: Calculate slope for Table2

Pick $(-2,10)$ and $(-4,4)$:
$m = \frac{4 - 10}{-4 - (-2)} = \frac{-6}{-2} = 3$

Step4: Calculate slope for Table3

Pick $(1,-5)$ and $(3,-2)$:
$m = \frac{-2 - (-5)}{3 - 1} = \frac{3}{2}$

Step5: Calculate slope for Table4

Pick $(-3,-1)$ and $(-2,-4)$:
$m = \frac{-4 - (-1)}{-2 - (-3)} = \frac{-3}{1} = -3$

Step6: Calculate slope for Table5

Pick $(3,-6)$ and $(0,-2)$:
$m = \frac{-2 - (-6)}{0 - 3} = \frac{4}{-3} = -\frac{4}{3}$

Step7: Calculate slope for Table6

Pick $(0,-3)$ and $(4,-2)$:
$m = \frac{-2 - (-3)}{4 - 0} = \frac{1}{4}$

Answer:

1. Slope = 5
2. Slope = 3
3. Slope = $\frac{3}{2}$
4. Slope = -3
5. Slope = $-\frac{4}{3}$
6. Slope = $\frac{1}{4}$

For the preference question: A common preferred method is using the slope formula with two clear points from the table, as it is direct and consistent for linear relationships.