Questions: Sketch a graph of f(x)=-2x-2

Transcript text: Sketch a graph of $f(x)=-2 x-2$

Solution

Solution Steps

Step 1: Identify the slope and y-intercept.

The given equation is in slope-intercept form, $f(x) = mx + b$, where $m$ is the slope and $b$ is the y-intercept. In this case, $m = -2$ and $b = -2$.

Step 2: Plot the y-intercept.

The y-intercept is the point where the graph crosses the y-axis. Since $b = -2$, the y-intercept is at the point $(0, -2)$.

Step 3: Use the slope to find another point.

The slope, $m = -2$, can be written as $-2/1$. This means that for every 1 unit we move to the right along the x-axis, we move down 2 units along the y-axis. Starting from the y-intercept $(0, -2)$, if we move 1 unit to the right, we get to $x = 1$, and moving 2 units down from $-2$ we get $y = -4$. So, another point on the line is $(1, -4)$.

Step 4: Draw the line.

Plot the two points, $(0, -2)$ and $(1, -4)$, on the graph and draw a straight line through them. This line represents the graph of $f(x) = -2x - 2$.