Question

graph the line.
$y + 3 = -\frac{2}{3}(x + 4)$

Explanation:

Step1: Identify the form of the equation

The given equation is \( y + 3 = -\frac{2}{3}(x + 4) \), which 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 \( m=-\frac{2}{3} \) and the point \( (x_1,y_1)=(- 4,-3) \).

Step2: Plot the point

On the coordinate plane, find the point with \( x=-4 \) and \( y = - 3 \) and mark it.

Step3: Use the slope to find another point

The slope \( m =-\frac{2}{3}=\frac{\text{rise}}{\text{run}} \). The rise is - 2 (which means we go down 2 units) and the run is 3 (which means we go to the right 3 units) from the point \( (-4,-3) \).
Starting from \( (-4,-3) \), moving down 2 units (so \( y=-3 - 2=-5 \)) and right 3 units (so \( x=-4 + 3=-1 \)), we get the point \( (-1,-5) \). We can also use the slope in the other direction: rise = 2 (up 2 units) and run=-3 (left 3 units). Starting from \( (-4,-3) \), moving up 2 units (\( y=-3 + 2=-1 \)) and left 3 units (\( x=-4-3=-7 \)), we get the point \( (-7,-1) \).

Step4: Draw the line

Draw a straight line passing through the points we found (e.g., \( (-4,-3) \), \( (-1,-5) \), \( (-7,-1) \)) to graph the line.

Answer:

To graph the line \( y + 3=-\frac{2}{3}(x + 4) \), first plot the point \((-4,-3)\). Then, using the slope \( -\frac{2}{3} \), find another point (e.g., from \((-4,-3)\), move down 2 units and right 3 units to get \((-1,-5)\) or up 2 units and left 3 units to get \((-7,-1)\)) and draw a straight line through these points.