Question

graph the line.
$y + 1 = -\frac{1}{4}(x + 5)$

Explanation:

Step1: Identify the form of the equation

The given equation \( y + 1 = -\frac{1}{4}(x + 5) \) is in the point - slope form \( y - y_1=m(x - x_1) \), where \( m \) is the slope and \( (x_1,y_1) \) is a point on the line. By comparing, we can see that \( m =-\frac{1}{4} \) and the point \( (x_1,y_1)=(- 5,-1) \).

Step2: Plot the point

First, we plot the point \( (-5,-1) \) on the coordinate plane.

Step3: Use the slope to find another point

The slope \( m =-\frac{1}{4}=\frac{\text{rise}}{\text{run}} \). The rise is - 1 (which means we go down 1 unit) and the run is 4 (which means we go right 4 units) from the point \( (-5,-1) \). So, starting from \( (-5,-1) \), if we go down 1 unit and right 4 units, we get the point \( (-5 + 4,-1-1)=(-1,-2) \). We can also go up 1 unit and left 4 units from \( (-5,-1) \) to get another point \( (-5-4,-1 + 1)=(-9,0) \).

Step4: Draw the line

After plotting two (or more) points on the line, we draw a straight line passing through these points.

Answer:

To graph the line \( y + 1 = -\frac{1}{4}(x + 5) \):

1. Plot the point \((-5,-1)\) (from the point - slope form \(y - y_1=m(x - x_1)\) where \(x_1=-5,y_1 = - 1,m=-\frac{1}{4}\)).
2. Use the slope \(m =-\frac{1}{4}\): from \((-5,-1)\), move down 1 unit and right 4 units to get \((-1,-2)\) (or move up 1 unit and left 4 units to get \((-9,0)\)).
3. Draw a straight line through the plotted points.