To rewrite the equation $18x + 8y = 5$ in slope-intercept form ($y = mx + b$), follow these steps:

Step 1: Isolate the $y$ term

Start by moving the $18x$ term to the right side of the equation:

$8y = -18x + 5$

Step 2: Solve for $y$

Next, divide every term by 8 to isolate $y$:

$y = -\frac{18}{8}x + \frac{5}{8}$

Step 3: Simplify the fractions

Simplify the fraction $\frac{18}{8}$ to $\frac{9}{4}$:

$y = -\frac{9}{4}x + \frac{5}{8}$

So, the equation in slope-intercept form is:

$y = -\frac{9}{4}x + \frac{5}{8}$

This form clearly shows the slope $m = -\frac{9}{4}$ and the y-intercept $b = \frac{5}{8}$.

Would you like to explore how this equation behaves on a graph, or do you have any other questions related to it?

Here are five related questions:

1. How would you find the x-intercept of this equation?
2. What is the significance of the slope in this equation?
3. Can you convert this slope-intercept form back into standard form?
4. How would this line compare to another line with a different slope?
5. What happens to the graph of the line if the slope is changed?

Tip: Understanding the slope-intercept form is useful for quickly determining the direction and steepness of a line on a graph.