Question

Find the equation of the linear function represented by the table below in slope-intercept form.
x y
11 11
22 55
33 99
44 1313

Answer 1

To find the equation of the linear function in slope-intercept form \( y = mx + b \), we first need to determine the slope \( m \) using the points from the table. We can use two points from the table to calculate the slope.

Let's use the points \( (11, 11) \) and \( (22, 55) \):

1. Calculate the slope \( m \):
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{55 - 11}{22 - 11} = \frac{44}{11} = 4
\]

2. Use the slope and one of the points to find the y-intercept \( b \). We can use the point \( (11, 11) \):
\[
11 = 4(11) + b
\]
\[
11 = 44 + b
\]
\[
b = 11 - 44 = -33
\]

So, the equation of the linear function in slope-intercept form is:
\[
y = 4x - 33
\]

Let's double-check the other points to ensure they fit this equation:

- For \( x = 22 \):
\[
y = 4(22) - 33 = 88 - 33 = 55 \quad \text{(correct)}
\]

- For \( x = 33 \):
\[
y = 4(33) - 33 = 132 - 33 = 99 \quad \text{(correct)}
\]

- For \( x = 44 \):
\[
y = 4(44) - 33 = 176 - 33 = 143 \quad \text{(does not match, correctly corresponding to interpretation of point)}
\]

The expected value at \( x = 44 \) looks like a misinterpretation in your data. It should have been \( y = 143 \) instead of \( 1313 \).

Therefore, based on our calculations and assumptions, the correct linear function that fits the provided pairs (except for the doubtful last entry) is:
\[
y = 4x - 33
\]