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Graph ​y−5=−23(x+9)​ using the point and slope given in the equation.

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

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To graph the equation \( y - 5 = -23(x + 9) \), we start by identifying the slope and the point given in the equation.

Step 1: Identify the point and slope

The equation is in point-slope form \( y - y_1 = m(x - x_1) \), where:

  • \( m \) is the slope,
  • \( (x_1, y_1) \) is a point on the line.

From the equation:

  • The point is \( (-9, 5) \) (since it is \( x + 9 \) which indicates \( x_1 = -9 \) and \( y_1 = 5 \)).
  • The slope \( m = -23 \).

Step 2: Use the slope to find another point

We can use the slope to find another point on the line:

  • Start at the point \( (-9, 5) \).
  • Since the slope is \( -23 \), for each unit you move to the right (increase in \( x \)), you move down \( 23 \) units (decrease in \( y \)).
  1. Move 1 unit to the right from \( x = -9 \) to \( x = -8 \): \[ y = 5 - 23(1) = 5 - 23 = -18 \] So, another point is \( (-8, -18) \).

Step 3: Plot the points

Now we have two points:

  1. Point 1: \( (-9, 5) \)
  2. Point 2: \( (-8, -18) \)

Step 4: Draw the line

  • Plot the points on the graph.
  • Draw a straight line through these points, extending it in both directions.

These steps will allow you to graph the line represented by the equation \( y - 5 = -23(x + 9) \) accurately.