Question

graph the line with the equation $y = -x - 2$.

Explanation:

Step1: Identify slope and y-intercept

The equation $y=-x-2$ is in slope-intercept form $y=mx+b$, where $m=-1$ (slope) and $b=-2$ (y-intercept).

Step2: Plot the y-intercept

The y-intercept is the point where $x=0$, so the point is $(0, -2)$. Mark this on the graph.

Step3: Use slope to find a second point

Slope $\frac{\Delta y}{\Delta x}=-1=\frac{-1}{1}$. From $(0,-2)$, move 1 unit right and 1 unit down to get the point $(1, -3)$. Mark this point.

Step4: Draw the line

Connect the two points $(0,-2)$ and $(1,-3)$, then extend the line in both directions across the coordinate plane.

Answer:

The line passes through points such as $(0, -2)$ and $(1, -3)$, with a slope of $-1$, extending across the entire coordinate grid.