Question

Find the equation of the linear function represented by the table below in slope-intercept form.
y
x
0
1
2
3
4
8
16
24
32
40

Answer 1

To find the equation of the linear function represented by the table, we need to find the slope and y-intercept.

We can use the slope formula, which is
slope = (change in y) / (change in x)

Looking at the table, we see that as x increases by 1, y increases by 8. So the change in y is 8 and the change in x is 1.

slope = (change in y) / (change in x) = 8 / 1 = 8

Now we can use the point-slope form of a linear equation, which is
y - y1 = m(x - x1)

Choosing any point from the table, we can use (0, 0) for convenience.

Using the point-slope form with the slope we found:
y - 0 = 8(x - 0)

This simplifies to:
y = 8x

Therefore, the equation of the linear function represented by the table in slope-intercept form is:
y = 8x