Question

Find the equation of the linear function represented by the table below in slope-intercept form.
y
x
0
1
2
3
4
-2
6
14
22
30
Answer
Attempt 1 out of 2

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Answer 1

To find the equation of the linear function represented by the table, we need to identify the slope (m) and the y-intercept (b) of the linear equation in the form \( y = mx + b \).

Given the x and y values from the table:

| x | y |
|---|----|
| 0 | -2 |
| 1 | 6 |
| 2 | 14 |
| 3 | 22 |
| 4 | 30 |

1. **Identify the slope (m)**: The slope can be calculated using any two points from the table. Let’s use the first two points (0, -2) and (1, 6).

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{6 - (-2)}{1 - 0} = \frac{8}{1} = 8
\]

2. **Identify the y-intercept (b)**: The y-intercept is the value of y when x = 0. From the table, when \( x = 0 \), \( y = -2 \). Therefore, b = -2.

3. **Write the equation**: Now we have the slope \( m = 8 \) and the y-intercept \( b = -2 \). We can write the equation as follows:

\[
y = 8x - 2
\]

Therefore, the equation of the linear function in slope-intercept form is:

\[
\boxed{y = 8x - 2}
\]