To find the linear equation that describes the relationship between $x$ and $y$ in the table, we can determine the equation of a line in the form:

$y = mx + b$

where:

• $m$ is the slope,
• $b$ is the y-intercept.

Step 1: Find the Slope ($m$)

The slope $m$ is the change in $y$ divided by the change in $x$.

Using two points from the table:

1. Points $(1, 16)$ and $(2, 17)$: $m = \frac{17 - 16}{2 - 1} = \frac{1}{1} = 1$

The slope $m$ is $1$.

Step 2: Find the Y-Intercept ($b$)

Using the equation $y = mx + b$ and one point from the table, substitute $x = 1$, $y = 16$, and $m = 1$:

$16 = 1 \cdot 1 + b$ $16 = 1 + b$ $b = 15$

Final Equation

The equation that represents the relationship in the table is:

$y = x + 15$

Would you like more details, or do you have any questions?

Related Questions

1. How do you find the slope of a line when given two points?
2. What does the y-intercept represent in a linear equation?
3. How can you verify if a given equation fits a table of values?
4. How would the equation change if the slope were different?
5. What other forms can linear equations take, besides $y = mx + b$?

Tip

Always check if the changes in $x$ and $y$ are consistent across points when determining if a relationship is linear.