The equation you provided is in the slope-intercept form $y = mx + b$, where $m$ is the slope, and $b$ is the y-intercept.

Given:

• $m = -2$
• $b = 2$

The equation becomes: $y = -2x + 2$

Steps to solve and graph:

1. Identify key points:

   • The y-intercept occurs when $x = 0$, so: $y = -2(0) + 2 = 2$ Thus, one point on the graph is $(0, 2)$.

   • The slope $m = -2$ means that for every 1 unit increase in $x$, $y$ decreases by 2 units.

2. Find another point: Choose another value of $x$, say $x = 1$: $y = -2(1) + 2 = 0$ So another point is $(1, 0)$.

3. Plot these points: Plot $(0, 2)$ and $(1, 0)$ on a graph, and draw a straight line through them, which represents the equation $y = -2x + 2$.

I can also graph this for you if you'd like to see the visual. Would you like a graph?

Here are some questions to think about:

1. How do changes in slope affect the steepness of the graph?
2. What would happen if the y-intercept was negative?
3. What is the significance of the slope in real-life applications?
4. How does a vertical shift affect the equation of a line?
5. Can you find the x-intercept of this line?

Tip: The slope tells you how fast the line rises or falls, and the y-intercept tells you where it crosses the y-axis.