To graph the equation $y = \frac{4}{5}x - 2$, let's follow these steps:

1. Identify the slope and y-intercept:

   • The equation is in slope-intercept form $y = mx + b$, where $m = \frac{4}{5}$ (the slope) and $b = -2$ (the y-intercept).
   • This means the line crosses the y-axis at $y = -2$.

2. Plot the y-intercept:

   • Start by plotting the point $(0, -2)$ on the coordinate plane.

3. Use the slope to find another point:

   • The slope $\frac{4}{5}$ means "rise over run." For each increase of 5 units in $x$, $y$ increases by 4 units.
   • Starting from $(0, -2)$, move 5 units to the right (to $x = 5$) and 4 units up. This gives you the point $(5, 2)$.

4. Plot the second point:

   • Place a point at $(5, 2)$.

5. Draw the line:

   • Draw a line through the points $(0, -2)$ and $(5, 2)$. This line represents the equation $y = \frac{4}{5}x - 2$.

Would you like further details on the steps or a visualization of the graph?

Additional Questions:

1. What does the slope of $\frac{4}{5}$ represent in practical terms?
2. How would the graph change if the slope were negative?
3. What would be the new line equation if the y-intercept was increased by 3 units?
4. Can you calculate where this line intersects the x-axis?
5. What is the equation of a line parallel to this one?

Tip: In slope-intercept form $y = mx + b$, the slope $m$ tells you how steep the line is, and $b$ gives you the starting point on the y-axis.