To graph a linear function with a slope of $3$ and a $y$-intercept of $10$, we start by using the slope-intercept form of a linear equation, which is:

$y = mx + b$

where:

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

Substituting the given values:

• Slope $m = 3$,
• $y$-intercept $b = 10$,

the equation becomes:

$y = 3x + 10$

To graph this:

1. Start at the $y$-intercept point, which is $(0, 10)$.
2. From this point, use the slope to find another point on the line. The slope $3$ means a rise of $3$ units for every $1$ unit run to the right. So, from $(0, 10)$, move up $3$ units and right $1$ unit to get the next point $(1, 13)$.
3. Plot these points and draw a straight line through them.

Would you like me to generate the graph for you?

---

Here are 5 related questions to consider:

1. What is the general formula for a linear equation?
2. How do you interpret the slope and $y$-intercept of a line?
3. What changes in the graph if the slope becomes negative?
4. How would the graph change if the $y$-intercept was $0$?
5. How can you determine if two lines are parallel?

Tip: The slope of a line shows how steep it is; a higher slope means a steeper line.