Question

Xavier is attempting to recreate a problem his teacher showed him in class. To do so, he creates the table below.

x
y
1
3
2
?

He remembers that the slope of the line through the ordered pairs in the table was 4. What is the missing y-value in the table?
5
7
8
12

Answer 1

To find the missing y-value, we can use the formula for the slope of a line given two points \((x_1, y_1)\) and \((x_2, y_2)\):

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

From the table, we have two points:
- \( (1, 3) \) (where \(x_1 = 1\) and \(y_1 = 3\))
- \( (2, y_2) \) (where \(x_2 = 2\) and \(y_2\) is the missing value)

Given that the slope is \(4\), we can set up the equation:

\[
4 = \frac{y_2 - 3}{2 - 1}
\]

This simplifies to:

\[
4 = y_2 - 3
\]

Now, solve for \(y_2\):

\[
y_2 = 4 + 3
\]
\[
y_2 = 7
\]

Thus, the missing \(y\)-value is \(7\).

So, the answer is **7**.