To write the equation of the line in slope-intercept form ($y = mx + b$), where $m$ is the slope and $b$ is the $y$-intercept, follow these steps:

Step 1: Find the slope ($m$)

The formula for slope between two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

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

Using the first two points $(0, 3)$ and $(1, 7)$:
$m = \frac{7 - 3}{1 - 0} = \frac{4}{1} = 4.$

So, the slope $m = 4$.

Step 2: Find the $y$-intercept ($b$)

The $y$-intercept is the value of $y$ when $x = 0$. From the table, when $x = 0$, $y = 3$.

Thus, $b = 3$.

Step 3: Write the equation

Substitute $m = 4$ and $b = 3$ into $y = mx + b$:

$y = 4x + 3.$

Final Answer:

The equation of the line is:

$\boxed{y = 4x + 3}.$

Do you need further clarification or details? Let me know!

Related Questions:

1. How do you find the slope if the $x$- and $y$-values are decimals?
2. What is the general form of a linear equation?
3. How do you graph the equation $y = 4x + 3$?
4. How can you check if all points lie on the same line?
5. How do you write an equation if the slope is negative?

Tip: Always double-check the slope by picking different pairs of points. If the slope is the same, the line is consistent.