Question

graph the following equation: y = -2 - 2x

Explanation:

Step1: Rewrite in slope-intercept form

The equation is already in the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept:
$y = -2x - 2$

Step2: Identify y-intercept

The y-intercept $b = -2$, so the line crosses the y-axis at the point $(0, -2)$.

Step3: Identify slope

The slope $m = -2$, which is equivalent to $\frac{-2}{1}$. This means for every 1 unit increase in $x$, $y$ decreases by 2 units.

Step4: Find a second point

Using the slope from the y-intercept: start at $(0, -2)$, move 1 unit right to $x=1$, then 2 units down to $y=-4$. This gives the point $(1, -4)$.
Alternatively, use $x=-1$: substitute $x=-1$ into the equation:
$y = -2(-1) - 2 = 2 - 2 = 0$, so the point $(-1, 0)$ is on the line.

Step5: Plot points and draw line

Plot the points $(0, -2)$ and $(-1, 0)$ (or $(1, -4)$), then draw a straight line through them.

Answer:

The line passes through points such as $(-1, 0)$ and $(0, -2)$, with a slope of $-2$, extending across the coordinate grid.