The image shows a problem about a linear function $h(x) = 5x + 4$, with parts (a) and (b) visible. Let's break it down:

Part (a): Determine the slope and y-intercept of the function.

• The function is in the form $h(x) = mx + b$, where:
  • $m$ is the slope.
  • $b$ is the y-intercept.

From the given equation $h(x) = 5x + 4$:

• The slope $m = 5$.
• The y-intercept $b = 4$.

Part (b): Use the slope and y-intercept to graph the linear function.

• To graph this, start at the y-intercept (0, 4) on the y-axis.
• Then, using the slope $m = 5$, rise 5 units and run 1 unit to the right to find another point (1, 9).
• Connect these two points with a straight line.

Would you like more details or assistance on any part?

Here are some follow-up questions:

1. How do you interpret the slope in a real-world context?
2. What happens to the graph if the slope is negative?
3. How can you verify the y-intercept using a table of values?
4. What is the significance of the x-intercept, and how can you find it?
5. How would the graph change if the slope were fractional, like $\frac{1}{2}$?

Tip: When graphing a line, always plot the y-intercept first, then use the slope to find additional points.