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: 1,3,5,7 and 9

And on the right is y with the numbers 11,16,21,26, and 31

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

Answer 1

When y increases by 5, x increases by 2

slope is rise over run, or change in y divided by change in x, so slope=m = 5/2

the y-intercept is the y value when x = 0 or (0,y) we know (1,11) is on the line, so reduce x by 1 and reduce y by 5/2, half the changes in the table

the y-intercept is 11- 5/2 = (22-5)/2 = 17/2

the equation is

y= 5x/2 + 17/2

Answer 2

Slope m = (y₂ - y₁)/(x₂ - x_{1) = (16 - 11)/(3 - 1) = 5/2.}

_{Linear function is y = 5/2x + b. To get b we use point (1, 11), so 11 = 5/2·1 + 11, b = 17/2.}

_{Our linear function y = 5/2x + 17/2; y-ntercept (0, 17/2)}