Question

Write the linear equation that gives the rule for this table.

x y
5 44
10 59
15 74
20 89


Write your answer as an equation with y first, followed by an equals sign.

Answer 1

To find the linear equation that represents the relationship between \(x\) and \(y\) in the given table, we can use the format of a linear equation:

\[ y = mx + b \]

where \(m\) is the slope and \(b\) is the y-intercept.

First, we will calculate the slope \(m\) using two points from the table:
1. \( (5, 44) \)
2. \( (10, 59) \)

The formula for the slope is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using our points:

\[
m = \frac{59 - 44}{10 - 5} = \frac{15}{5} = 3
\]

Now, we have the slope \(m = 3\).

Next, we'll use one of the points to solve for \(b\). Let's use the point \( (5, 44) \):

\[
44 = 3(5) + b
\]
\[
44 = 15 + b
\]
\[
b = 44 - 15 = 29
\]

Now, we can write the equation:

\[
y = 3x + 29
\]

So, the final linear equation is:

\[
y = 3x + 29
\]