Graph the equation y-3=-3/2(x+4)
To graph the equation y - 3 = -3/2(x + 4), we can start by rearranging it into slope-intercept form: y = mx + b. Here, m represents the slope and (0, b) represents the y-intercept.
y - 3 = -3/2(x + 4)
To simplify, we first distribute -3/2 to both terms in the parentheses:
y - 3 = -3/2x - 3(2)
y - 3 = -3/2x - 6
Next, we can move -3 to the left side of the equation by adding 3 to both sides:
y - 3 + 3 = -3/2x - 6 + 3
y = -3/2x - 3
Now we can see that the slope (m) is -3/2 and the y-intercept (b) is -3.
To graph this equation, we can start by plotting the y-intercept at (0, -3).
Next, we can use the slope to find additional points. The slope -3/2 can be written as a fraction -3/2 = -3 รท 2 = -1.5. This means that for every 2 units you move to the right, you move down 3 units.
Using this information, we can plot two more points: 2 units to the right and 3 units down from the y-intercept at (0, -3), and 4 units to the right and 6 units down from the y-intercept.
This gives us the points (0, -3), (2, -6), and (4, -9).
Finally, we can connect these points with a straight line to create the graph of the equation.
Here is the graph: