graph this line using the slope and y - intercept: y = - 2x - 3 click to select points on the graph.

Answer

Answer:

To graph ( y = -2x - 3 ), first identify the ( y )-intercept and slope. The ( y )-intercept ( b=-3 ), so one point is ( (0,-3) ). The slope ( m = -2=\frac{-2}{1} ). From ( (0,-3) ), move 1 unit to the right (increase ( x ) by 1) and 2 units down (decrease ( y ) by 2) to get the point ( (1,-5) ). Another point: from ( (0,-3) ), move 1 unit to the left (decrease ( x ) by 1) and 2 units up (increase ( y ) by 2) to get ( (-1,-1) ). Plot these points ( (0,-3) ), ( (1,-5) ), ( (-1,-1) ) and draw a straight line through them.

Explanation:

Step1: Identify ( y )-intercept

The equation is in slope - intercept form ( y=mx + b ). For ( y=-2x - 3 ), ( b=-3 ). So the line crosses the ( y )-axis at ( (0,-3) ).

Step2: Use the slope to find other points

The slope ( m=-2=\frac{\Delta y}{\Delta x} ). From ( (0,-3) ):

If ( \Delta x = 1 ), then ( \Delta y=-2 ). New point: ( (0 + 1,-3-2)=(1,-5) ).
If ( \Delta x=-1 ), then ( \Delta y = 2 ). New point: ( (0-1,-3 + 2)=(-1,-1) ).

Step3: Plot and draw the line

Plot ( (0,-3) ), ( (1,-5) ), ( (-1,-1) ) on the coordinate plane. Then draw a straight line passing through these points. This line represents the equation ( y=-2x - 3 ).