Question

17 graph the equation: $y = -\frac{1}{3}x - 4$

Explanation:

Step1: Identify the slope and y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For the equation \(y=-\frac{1}{3}x - 4\), the slope \(m =-\frac{1}{3}\) and the y - intercept \(b=- 4\).

Step2: Plot the y - intercept

The y - intercept is \((0,b)\). Since \(b = - 4\), we plot the point \((0,-4)\) on the y - axis.

Step3: Use the slope to find another point

The slope \(m=-\frac{1}{3}=\frac{\text{rise}}{\text{run}}\). The rise is \(- 1\) (down 1 unit) and the run is \(3\) (right 3 units) from the y - intercept \((0,-4)\). So, starting from \((0,-4)\), moving down 1 unit and right 3 units gives the point \((0 + 3,-4-1)=(3,-5)\). We can also use a positive run and negative rise: moving up 1 unit (rise = 1) and left 3 units (run=-3) from \((0,-4)\) gives the point \((0 - 3,-4 + 1)=(-3,-3)\).

Step4: Draw the line

Draw a straight line through the points we have plotted (e.g., \((0,-4)\) and \((3,-5)\) or \((0,-4)\) and \((-3,-3)\)).

Answer:

To graph \(y =-\frac{1}{3}x-4\):

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