Writing equations of linear functions

Question

Writing equations of linear functions, please help! 

The chart below is asking what the slope, y intercept, and equations are. 

In the first chart it has x on the left and underneath are the numbers: 2,4,6,8,10 and 

And on the right is y with the numbers 8,9,10,11 and 12

How would I identify the slope, y intercept, and equation for this problem?

Answer 1

the x-values are 2,4,6,8,10

the y-values are 8,9,10,11,12

pair the first x-value with the first y-value

pair the second x-value with the second y-value

and so on to get ordered pairs of numbers

(2,8), (4,9), (6,10), (8,11), and (10,12)

choose any two ordered pairs and find the slope: (y₂-y₁)/(x₂-x₁)

(2,8) and (4,9) for example

(9-8)/(4-2)=1/2 which is the slope

(6,10) and (10,12) for another example

(12-10)/(10-6)=2/4= 1/2 again

use y=mx+b where m=slope and b=y-intercept

y=(1/2)x+b

now use any ordered pair and substitute the values for x and y to find b

using (4,9) we get 9=(1/2)(4)+b

9=2+b

b=9-2

b=7 which is the y-intercept

y=(1/2)x+7 is the equation

1/2 is the slope

7 is the y-intercept

Answer 2

(2,8) and (4,9) Two points on the line.

x increasing by 2

y increasing by one

slope change of y divided by change in x

1/2 is the slope (m)

if you look at the pattern you will see the point (0,7) would have been the previous point.

you can also substitute in one point to find the y - intercept.

y = Mx + b

8 = 1/2(2) + b

8 = 1 + b subtract 1

7 = b

y = 1/2x + 7

hope it helps

Dennis