Question

graph the line. y = -x - 4

Explanation:

Step1: Identify the slope and y - intercept

The equation of the line is in the slope - intercept form \(y = mx + b\), 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 coordinate plane.

Step3: Use the slope to find another point

The slope \(m=\frac{\text{rise}}{\text{run}}=-1=\frac{- 1}{1}\) or \(\frac{1}{-1}\). Starting from the point \((0,-4)\), if we use the slope \(\frac{\text{rise}}{\text{run}}=\frac{-1}{1}\), we move down 1 unit (because the rise is - 1) and then 1 unit to the right (because the run is 1). This gives us the point \((0 + 1,-4-1)=(1,-5)\). If we use the slope \(\frac{1}{-1}\), we move up 1 unit and 1 unit to the left, getting the point \((0 - 1,-4 + 1)=(-1,-3)\).

Step4: Draw the line

Draw a straight line through the points that we have plotted (e.g., \((0,-4)\), \((1,-5)\), \((-1,-3)\)) to graph the line \(y=-x - 4\).

(Note: Since this is a graphing problem, the final answer is the graph of the line \(y =-x-4\) passing through points like \((0,-4)\), \((1,-5)\), \((-1,-3)\) etc. If we were to describe it in terms of key features, the line has a slope of - 1 and a y - intercept at \((0,-4)\))

Answer:

Step1: Identify the slope and y - intercept

The equation of the line is in the slope - intercept form \(y = mx + b\), 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 coordinate plane.

Step3: Use the slope to find another point

The slope \(m=\frac{\text{rise}}{\text{run}}=-1=\frac{- 1}{1}\) or \(\frac{1}{-1}\). Starting from the point \((0,-4)\), if we use the slope \(\frac{\text{rise}}{\text{run}}=\frac{-1}{1}\), we move down 1 unit (because the rise is - 1) and then 1 unit to the right (because the run is 1). This gives us the point \((0 + 1,-4-1)=(1,-5)\). If we use the slope \(\frac{1}{-1}\), we move up 1 unit and 1 unit to the left, getting the point \((0 - 1,-4 + 1)=(-1,-3)\).

Step4: Draw the line

Draw a straight line through the points that we have plotted (e.g., \((0,-4)\), \((1,-5)\), \((-1,-3)\)) to graph the line \(y=-x - 4\).

(Note: Since this is a graphing problem, the final answer is the graph of the line \(y =-x-4\) passing through points like \((0,-4)\), \((1,-5)\), \((-1,-3)\) etc. If we were to describe it in terms of key features, the line has a slope of - 1 and a y - intercept at \((0,-4)\))