Question

graph the line.
$y = -dfrac{3}{2}x - 3$

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 \(y=-\frac{3}{2}x - 3\), the slope \(m =-\frac{3}{2}\) and the y - intercept \(b=- 3\).

Step2: Plot the y - intercept

The y - intercept is \(b = - 3\), so we plot the point \((0,-3)\) on the coordinate plane.

Step3: Use the slope to find another point

The slope \(m=-\frac{3}{2}=\frac{\text{rise}}{\text{run}}\). The rise is \(- 3\) (down 3 units) and the run is \(2\) (right 2 units) from the point \((0,-3)\). So from \((0,-3)\), moving down 3 units and right 2 units, we get the point \((0 + 2,-3-3)=(2,-6)\). We can also use a positive rise and negative run: rise \(= 3\) (up 3 units) and run \(=-2\) (left 2 units) from \((0,-3)\) to get the point \((0-2,-3 + 3)=(-2,0)\).

Step4: Draw the line

Draw a straight line through the points we have plotted (e.g., \((0,-3)\) and \((2,-6)\) or \((0,-3)\) and \((-2,0)\)) and extend it in both directions.

To graph the line:

1. Plot the point \((0,-3)\) (since when \(x = 0\), \(y=-3\)).
2. From \((0,-3)\), use the slope \(m =-\frac{3}{2}\). Move 2 units to the right (run) and 3 units down (rise) to get the point \((2,-6)\), or 2 units to the left and 3 units up to get \((-2,0)\).
3. Draw a straight line connecting these points (and extending it) to represent the line \(y =-\frac{3}{2}x-3\).

(Note: Since the question is about graphing, the final answer is the graph of the line \(y =-\frac{3}{2}x - 3\) with a y - intercept at \((0,-3)\) and passing through other points like \((2,-6)\) or \((-2,0)\) etc.)

Answer:

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 \(y=-\frac{3}{2}x - 3\), the slope \(m =-\frac{3}{2}\) and the y - intercept \(b=- 3\).

Step2: Plot the y - intercept

The y - intercept is \(b = - 3\), so we plot the point \((0,-3)\) on the coordinate plane.

Step3: Use the slope to find another point

The slope \(m=-\frac{3}{2}=\frac{\text{rise}}{\text{run}}\). The rise is \(- 3\) (down 3 units) and the run is \(2\) (right 2 units) from the point \((0,-3)\). So from \((0,-3)\), moving down 3 units and right 2 units, we get the point \((0 + 2,-3-3)=(2,-6)\). We can also use a positive rise and negative run: rise \(= 3\) (up 3 units) and run \(=-2\) (left 2 units) from \((0,-3)\) to get the point \((0-2,-3 + 3)=(-2,0)\).

Step4: Draw the line

Draw a straight line through the points we have plotted (e.g., \((0,-3)\) and \((2,-6)\) or \((0,-3)\) and \((-2,0)\)) and extend it in both directions.

To graph the line:

1. Plot the point \((0,-3)\) (since when \(x = 0\), \(y=-3\)).
2. From \((0,-3)\), use the slope \(m =-\frac{3}{2}\). Move 2 units to the right (run) and 3 units down (rise) to get the point \((2,-6)\), or 2 units to the left and 3 units up to get \((-2,0)\).
3. Draw a straight line connecting these points (and extending it) to represent the line \(y =-\frac{3}{2}x-3\).

(Note: Since the question is about graphing, the final answer is the graph of the line \(y =-\frac{3}{2}x - 3\) with a y - intercept at \((0,-3)\) and passing through other points like \((2,-6)\) or \((-2,0)\) etc.)