Question

graph the line.
-2x + y = 2

Explanation:

Step1: Rewrite in slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.
Starting with the equation $-2x + y=2$, we can solve for $y$ by adding $2x$ to both sides of the equation.
We get $y = 2x+2$.

Step2: Identify the y - intercept

In the equation $y = 2x + 2$, the y - intercept $b = 2$. This means the line crosses the y - axis at the point $(0,2)$.

Step3: Identify the slope

The slope $m = 2=\frac{2}{1}$. The slope is the rise over run, which means for every 1 unit we move to the right (run) along the x - axis, we move up 2 units (rise) along the y - axis.
From the y - intercept $(0,2)$, if we move 1 unit to the right (to $x = 1$) and 2 units up, we get the point $(1,4)$. We can also find another point by moving in the opposite direction. If we move 1 unit to the left (to $x=- 1$) and 2 units down, we get the point $(-1,0)$.

Step4: Graph the line

Plot the points $(0,2)$, $(1,4)$ and $(-1,0)$ (or any two of these points) on the coordinate plane and then draw a straight line through them.

Answer:

To graph the line $y = 2x + 2$:

1. Plot the y - intercept at $(0,2)$.
2. Use the slope (rise = 2, run = 1) to find another point, e.g., from $(0,2)$, move 1 unit right and 2 units up to get $(1,4)$ (or 1 unit left and 2 units down to get $(-1,0)$).
3. Draw a straight line through the plotted points.