Question

find the slopes of the equation and the table. do they have the same slope?
y = x - 6

x	8	9	4	5	6	10
y	-2	-1	0	1	2	6

show your work here

slope of equation =
slope of table =

○ yes, the slopes are the same. ○ no, the slopes are not the same.

Explanation:

Step1: Find slope of equation \( y = x - 6 \)

The equation is in slope - intercept form \( y=mx + b \), where \( m \) is the slope. For \( y=x - 6 \), comparing with \( y = mx + b \), we have \( m = 1 \). So the slope of the equation is \( 1 \).

Step2: Find slope of the table

We use the slope formula \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Let's take two points from the table. Let's take \( (x_1,y_1)=(8, - 2) \) and \( (x_2,y_2)=(9,-1) \).
Substitute into the slope formula: \( m=\frac{-1-(-2)}{9 - 8}=\frac{-1 + 2}{1}=\frac{1}{1}=1 \). We can check with other points, for example, \( (x_1 = 9,y_1=-1) \) and \( (x_2 = 10,0) \), \( m=\frac{0-(-1)}{10 - 9}=\frac{1}{1}=1 \). So the slope of the table is \( 1 \).

Step3: Compare the slopes

The slope of the equation is \( 1 \) and the slope of the table is \( 1 \). So the slopes are the same.

Answer:

Slope of equation \( = 1 \)
Slope of table \( = 1 \)
Yes, the slopes are the same.