Question

graph this line using the slope and y-intercept:
y = -x - 4
click to select points on the graph.

Explanation:

Step1: Identify slope and y - intercept

The equation of a line in slope - intercept form is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For the equation \(y=-x - 4\), we can rewrite it as \(y=(-1)x+(-4)\). So, the slope \(m=-1\) and the y - intercept \(b = - 4\).

Step2: Plot the y - intercept

The y - intercept is the point where the line crosses the y - axis. When \(x = 0\), \(y=-4\). So we plot the point \((0,-4)\) on the graph.

Step3: Use the slope to find another point

The slope \(m=-1=\frac{-1}{1}=\frac{\text{rise}}{\text{run}}\). From the point \((0, - 4)\), we can go down 1 unit (because the rise is - 1) and then right 1 unit (because the run is 1) to get the next point. So, from \((0,-4)\), moving down 1 and right 1 gives us the point \((1,-5)\). We can also go up 1 unit and left 1 unit (since \(\frac{-1}{1}=\frac{1}{-1}\)) from \((0,-4)\) to get the point \((-1,-3)\).

Step4: Draw the line

After plotting at least two points (e.g., \((0,-4)\) and \((1,-5)\) or \((0,-4)\) and \((-1,-3)\)), we draw a straight line passing through these points.

Answer:

To graph \(y=-x - 4\):

1. Plot the y - intercept \((0,-4)\).
2. Use the slope \(m = - 1\) to find another point (e.g., from \((0,-4)\), move down 1 and right 1 to get \((1,-5)\) or up 1 and left 1 to get \((-1,-3)\)).
3. Draw a straight line through the plotted points.