To graph the line given by the equation $y = -5x + 8$, let’s go through the steps:

1. Identify the slope and y-intercept:

   • The equation is in slope-intercept form, $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
   • Here, $m = -5$ and $b = 8$.

2. Plot the y-intercept:

   • The y-intercept is $8$, so place a point at $(0, 8)$ on the y-axis.

3. Use the slope to find another point:

   • The slope $-5$ can be interpreted as $-5/1$, meaning that for every 1 unit moved to the right (positive x-direction), we move 5 units down (negative y-direction).
   • Starting from $(0, 8)$, move 1 unit to the right to $x = 1$, then move 5 units down to $y = 3$. Place another point at $(1, 3)$.

4. Draw the line:

   • Connect the points $(0, 8)$ and $(1, 3)$ with a straight line, extending it in both directions.

This line represents the equation $y = -5x + 8$ on the graph.

Would you like further details on graphing lines or the reasoning behind each step?

Here are some related questions you might find helpful:

1. How do you graph lines with positive slopes?
2. What is the general form of a line, and how is it different from the slope-intercept form?
3. How would the graph change if the slope were less steep, like $y = -2x + 8$?
4. How do you graph a line given in standard form, such as $Ax + By = C$?
5. What is the effect of changing the y-intercept in a linear equation?

Tip: When working with a slope, remember that a negative slope means the line goes downward from left to right.