To find the linear equation that defines $y$ in terms of $x$, follow these steps:

Step 1: Identify Two Points

From the table, we have the points:
$(0,5), (1,6), (2,7), (3,8)$

Step 2: Find the Slope $m$

The slope formula is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Using points $(0,5)$ and $(1,6)$:

$m = \frac{6 - 5}{1 - 0} = \frac{1}{1} = 1$

Step 3: Use the Slope-Intercept Form

The general equation of a line is:

$y = mx + b$

We found $m = 1$. Now, using the point $(0,5)$:

$5 = 1(0) + b$

$b = 5$

Step 4: Write the Equation

$y = x + 5$

Step 5: Identify the y-Intercept

The y-intercept is where $x = 0$, which is:

$(0,5)$

Final Answer:

Equation: $y = x + 5$
y-Intercept: $(0,5)$

Would you like further explanation or examples?

Related Questions:

1. How do you determine if a table represents a linear function?
2. What happens if the slope is negative?
3. Can you write a linear equation given any two points?
4. How do you find the x-intercept of a linear equation?
5. How does changing the slope affect the graph of a line?

Tip: In a linear equation $y = mx + b$, the coefficient $m$ represents the rate of change, and $b$ represents the starting value when $x = 0$.