Question

graph the line with y-intercept -4 and slope -2.

Explanation:

Step1: Recall 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 that the slope $m=-2$ and the $y$-intercept $b = - 4$, the equation of the line is $y=-2x - 4$.

Step2: Plot the y - intercept

The $y$-intercept is $-4$, so we plot the point $(0,-4)$ on the $y$-axis.

Step3: Use the slope to find another point

The slope $m=-2=\frac{-2}{1}=\frac{\text{rise}}{\text{run}}$. From the point $(0, - 4)$, we move down 2 units (because the rise is - 2) and then 1 unit to the right (because the run is 1). This gives us the point $(0 + 1,-4-2)=(1,-6)$. We can also move up 2 units and left 1 unit from $(0,-4)$ to get the point $(-1,-2)$.

Step4: Draw the line

Draw a straight line passing through the points we found (e.g., $(0,-4)$ and $(1,-6)$ or $(0,-4)$ and $(-1,-2)$).

Answer:

To graph the line:

1. Plot the point \((0, - 4)\) (the \(y\)-intercept).
2. Use the slope \(-2=\frac{-2}{1}\): from \((0, - 4)\), move down 2 units and right 1 unit to get \((1, - 6)\), or up 2 units and left 1 unit to get \((-1, - 2)\).
3. Draw a straight line through these points.