Question

-2x + y = 2

Explanation:

Step1: Rewrite the equation 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.
Given the equation $-2x + y=2$, we can solve for $y$ by adding $2x$ to both sides of the equation.
So, $y=2x + 2$.

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 = 1), we move up 2 units (rise = 2).
Starting 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 the x - intercept by setting $y = 0$ in the equation $y=2x + 2$.
$0=2x+2$, subtract 2 from both sides: $- 2=2x$, then divide by 2: $x=- 1$. So the line also passes through the point $(-1,0)$.

To graph the line, we plot the points $(0,2)$ and $(-1,0)$ (or $(1,4)$) and draw a straight line through them.

(Note: Since the problem is about graphing the line, the key steps are to find the intercepts or use the slope - intercept form to find points on the line. The final answer in terms of graphing is to plot the line $y = 2x+2$ which passes through $(0,2)$ and $(-1,0)$ (among other points) and draw a straight line through these points.)

Answer:

The line $y = 2x + 2$ (rewritten from $-2x + y = 2$) is graphed by plotting the y - intercept $(0,2)$ and using the slope (rise = 2, run = 1) to find additional points (e.g., $(1,4)$ or $(-1,0)$) and drawing a straight line through them.