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, 2, 3, 4, and 5 

And on the right is y with the numbers 6.4, 7.2, 8.0, 8.8, and 9.6

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

Answer 1

You can examine the table to determine that indeed this table represents a linear function. As x increases in value by 1, the y values are going up by a value of 0.8. You can pick any two points in the table to calculate the slope as change in y over change in x. For example:

(9.6 - 6.4)/ (5 -1) = 3.2/4 = 0.8. Try that with two other points to convince yourself.

Now use the point-slope formula to write the equation of the line (at least this is one way to help determine the y -intercept. Let's use the point (1, 6.4)

y - 6.4 = 0.8(x -1)

y -6.4 =0.8x - 0.8

y = 0.8x -0.8 + 6.4

y = (4/5) x + 5.6

so the y-intercept is (0, 5.6).

Here is a link to a Desmos graph to help you see all of the above:

desmos.com/calculator/s0lpp1kco6

Answer 2

(1, 6.4)

(2, 7.2)

(3, 8.0)

(4, 8.8)

(5, 9,6)

The slope defines the change in y over the change in x, rise over run.

m = Δy/Δx = (y₂ - y₁)/(x₂ - x₁)

m = (7.2 - 6.4)/(2 - 1) = 0.8/1 = 0.8

m = (8.0 - 7.2)/(3 - 2) = 0.8/1 = 0.8

m = (8.8 - 8.0)/(4 - 3) = 0.8/1 = 0.8

m = (9.6 - 8.8)/(5 - 4) = 0.8/1 = 0.8

The y-intercept will be the value when x = 0. From the chart, x = 1 goes to y = 6.4. Each time we add 1, we increase the y-value by 0.8. In this case, we will decrease the y-value by 0.8. Therefore, when x = 0 then y = 5.6.

The slope is 0.8 or 4/5, the y-intercept is @ (0, 5.6), and the equation is y = 0.8x + 5.6 .