Let's first find the slope and y-intercept of the linear relationship shown in the table.

The formula for the slope ($m$) of a line is: $m = \frac{y_2 - y_1}{x_2 - x_1}$

Let's use the two points $(5, 16.5)$ and $(7, 21.5)$ from the table: $m = \frac{21.5 - 16.5}{7 - 5} = \frac{5}{2} = 2.5$

So, the slope ($m$) is 2.5.

Now, we use the slope-intercept form of the equation of a line, $y = mx + b$, to find the y-intercept ($b$).

We already know that $m = 2.5$. Using one of the points, say $(5, 16.5)$: $y = mx + b$ $16.5 = 2.5(5) + b$ $16.5 = 12.5 + b$ $b = 16.5 - 12.5 = 4$

Thus, the y-intercept is 4.

Summary:

• The slope is 2.5.
• The y-intercept is 4.

Would you like more details or have any questions?

Here are 5 related questions:

1. How would the slope change if the difference between the y-values increased?
2. Can you use the equation of the line to predict the value of $y$ when $x = 10$?
3. How would the graph of the line look based on the slope and y-intercept?
4. What is the interpretation of the slope in real-world scenarios?
5. How can you find the slope from any two points on a line?

Tip: The slope tells you how much $y$ changes for each unit increase in $x$.