The given function is $y = 4x + 7$.

To find the y-intercept, we set $x = 0$ because the y-intercept occurs where the graph crosses the y-axis, and at this point, the value of $x$ is zero.

Substitute $x = 0$ into the equation:

$y = 4(0) + 7 = 0 + 7 = 7$

Thus, the y-intercept is $7$. In coordinate form, it is $(0, 7)$.

Would you like more details on how this relates to the slope-intercept form of a line?

Here are 5 related questions:

1. What is the slope of the function $y = 4x + 7$?
2. How do you find the x-intercept of $y = 4x + 7$?
3. What is the general form of a linear equation, and how does it differ from the slope-intercept form?
4. How does the y-intercept change if the equation is $y = 4x - 3$?
5. How would you graph the line $y = 4x + 7$?

Tip: The y-intercept of a linear equation in the form $y = mx + b$ is always $b$.