To graph the line given by the equation $y = -4x + 2$, we can follow these 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, the slope $m = -4$ and the y-intercept $b = 2$.

2. Plot the y-intercept:

   • The y-intercept is the point where the line crosses the y-axis. Since $b = 2$, plot the point $(0, 2)$ on the graph.

3. Use the slope to find another point:

   • The slope $m = -4$ means that for every 1 unit you move to the right along the x-axis, you move 4 units down (since the slope is negative).
   • Starting from $(0, 2)$, move 1 unit to the right to $x = 1$, then move 4 units down to $y = -2$. This gives you another point $(1, -2)$.

4. Draw the line:

   • Plot the points $(0, 2)$ and $(1, -2)$.
   • Use a ruler to draw a straight line through these points. Extend the line in both directions to cover the graph.

I'll now graph the line on the given coordinate plane.

Here is how it looks:

1. The line crosses the y-axis at $(0, 2)$.
2. It passes through the point $(1, -2)$.
3. The line is drawn with a negative slope, so it goes down as you move from left to right.

Would you like to see the graph or have any further details?

Here are some related questions:

1. What does the slope of a line represent in a graph?
2. How can you determine the slope from two given points on a line?
3. How would the graph change if the slope were positive instead of negative?
4. How can you graph a line given in point-slope form?
5. What is the significance of the y-intercept in different types of linear equations?

Tip: When graphing lines, always check the slope and y-intercept first—they are the keys to drawing the graph accurately.