Let's solve the given equation step by step:

The given equation is:

$5x + 8y - 40 = 0$

a. Rewrite the equation in slope-intercept form (i.e., $y = mx + b$).

We start by isolating $y$:

1. Move the term $5x$ and $-40$ to the other side:

   $8y = -5x + 40$

2. Now, divide every term by 8 to solve for $y$:

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

So, the slope-intercept form of the equation is:

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

b. Find the slope and y-intercept.

From the slope-intercept form $y = mx + b$:

• The slope $m = -\frac{5}{8}$
• The y-intercept $b = 5$

c. Graphing the line.

To graph the line, you would:

1. Start at the y-intercept (0, 5) on the y-axis.
2. Use the slope $-\frac{5}{8}$ to find another point: go down 5 units (since the slope is negative) and right 8 units to plot another point.
3. Draw a straight line through these points.

Would you like any further details on the graphing or any clarification?

Here are 5 related questions:

1. How do you convert any standard form equation to slope-intercept form?
2. What does the slope tell you about the direction of a line?
3. How do you find the x-intercept of this line?
4. Can you graph a line using only the intercepts?
5. What happens to the graph if the slope is positive?

Tip: When graphing lines, always plot at least two points to ensure accuracy!