Question

99 points. What is the slope-intercept form of the function described by this table?

x 1 2 3 4
y 8 13 18 23
Enter your answer in the boxes. y = x + ???????

Answer 1

Use two of the sets of values in the table:

lets use the first set and the last set:

(1,8) and (4,23)

First find the slope, which is the change in Y over the change in X:

Slope = 23 - 8 / 4-1 = 15/3 = 5

The slope is 5.

Now we can find the equation of the line, using the equation of a line y -y1 = m(x-x1)

m is the slope, y1 would be the first y value, which is 8 and x1 is the first x value which is 1

so now we have y-8 = 5(x-1)

Simplify the right side"

y-8 = 5x-5

Add 8 to both sides:

y = 5x -5 +8

Simplify:

y =5x +3

Answer 2

y = 5x+3

Explanation:

To find the slope, we need to points

(1,8) and (2,13)

Slope is given by

m = (y2-y1)/(x2-x1)

= (13-8)/(2-1)

= 5/1

The slope is 5

We can use the point slope form for an equation

y-y1 = m(x-x1)

y-8 = 5(x-1)

Distribute the 5

y-8 = 5x-5

Add 8 to each side

y-8+8 = 5x-5+8

y = 5x+3

This is in slope intercept form