Ask a New Question
Menu

Graph ​y−5=−2/3(x+9)​ using the point and slope given in the equation.

Use the line tool and select two points on the line.

1 answer

To graph the equation \( y - 5 = -\frac{2}{3}(x + 9) \) using the point and slope given, we first rewrite it in the slope-intercept form \( y = mx + b \):

  1. Distribute the slope on the right side: \[ y - 5 = -\frac{2}{3}x - 6 \]

  2. Add 5 to both sides: \[ y = -\frac{2}{3}x - 1 \]

Now we can identify the following:

  • The slope \( m = -\frac{2}{3} \)
  • The y-intercept (where the line crosses the y-axis) is at \( b = -1 \), which corresponds to the point \( (0, -1) \).

Next, we also have a point given in the original equation:

  • The point \( (-9, 5) \) (found from the equation when \( x = -9 \), \( y = 5 \)).

Steps to graph the line:

  1. Plot the point (-9, 5) on the graph.
  2. Plot the y-intercept (0, -1) on the graph.
  3. Using the slope \( -\frac{2}{3} \):
    • From the point (0, -1), you move down 2 units (because of the negative sign) and to the right 3 units to find another point on the line. This would lead you to the point (3, -3).
  4. Connect the points (-9, 5), (0, -1), and (3, -3) with a straight line.

Selecting two points over the line:

  1. Point 1: (-9, 5)
  2. Point 2: (0, -1)

Finally, draw the line through these two points, which will extend infinitely in both directions, representing the graph of the linear equation.

If you wish to visualize this graphically, you would typically use graphing software or tools, but the steps above provide you with the methodology on how to graph the line using the given equation.