graph this line using the slope and y - intercept:\n\n$y=-\\frac{1}{2}x - 2$\n\nclick to select points on…

graph this line using the slope and y - intercept:\n\n$y=-\\frac{1}{2}x - 2$\n\nclick to select points on the graph.

graph this line using the slope and y - intercept:\n\n$y=-\\frac{1}{2}x - 2$\n\nclick to select points on the graph.

Answer

Answer:

To graph ( y = -\frac{1}{2}x - 2 ):

  1. Plot the ( y )-intercept:
    • The ( y )-intercept is ( - 2 ). So, plot the point ( (0,-2) ).
  2. Use the slope to find another point:
    • The slope ( m=-\frac{1}{2}=\frac{\text{rise}}{\text{run}} ).
    • From the point ( (0,-2) ), since the slope is ( -\frac{1}{2} ), we can move ( 2 ) units to the right (run ( = 2 )) and ( 1 ) unit down (rise (=- 1 )). This gives us the point ( (2,-3) ).
  3. Draw the line:
    • Connect the points ( (0,-2) ) and ( (2,-3) ) and extend the line in both directions.

Explanation:

Step1: Identify the ( y )-intercept

The equation of the line is in the slope - intercept form ( y = mx + b ), where ( b ) is the ( y )-intercept. For ( y=-\frac{1}{2}x - 2 ), ( b=-2 ). So, one point on the line is ( (0,-2) ).

Step2: Use the slope to find a second point

The slope ( m =-\frac{1}{2} ). Starting from ( (0,-2) ), if we increase ( x ) by ( 2 ) (run ( = 2 )), then ( y ) decreases by ( 1 ) (since ( m=\frac{\Delta y}{\Delta x}=-\frac{1}{2}), so ( \Delta y=-\frac{1}{2}\times\Delta x ), when ( \Delta x = 2 ), ( \Delta y=-1 )). So, the second point is ( (2,-3) ).

Step3: Draw the line

A straight line is determined by two points. Connect ( (0,-2) ) and ( (2,-3) ) and extend it. This line represents the graph of ( y =-\frac{1}{2}x - 2 ).