Find the equation of the linear function represented by the table below in slope-intercept form.

y
x
0
1
2
3
4
-1
4
9
14
19

1 answer

To find the equation of a linear function in slope-intercept form (y = mx + b), we need to determine the values of the slope (m) and the y-intercept (b).

We can use any two points from the table to calculate the slope. Let's use the points (1, 4) and (3, 9):

m = (y2 - y1) / (x2 - x1)
m = (9 - 4) / (3 - 1)
m = 5 / 2

Now that we have the slope (m = 5/2), we can substitute it into the slope-intercept form:

y = mx + b
4 = (5/2)(1) + b

To solve for b, we can rearrange the equation and isolate b:

4 - (5/2)(1) = b
4 - 5/2 = b
(8/2) - (5/2) = b
3/2 = b

Now we have the value of the y-intercept (b = 3/2). Therefore, the equation of the linear function represented by the table is:

y = (5/2)x + (3/2)