graph the line for $y - 6 = -4(x + 2)$ on the coordinate plane.
graph the line for $y - 6 = -4(x + 2)$ on the coordinate plane.
Answer
Answer:
To graph the line (y - 6=-4(x + 2)), first identify a point on the line and the slope.
Explanation:
Step1: Identify the point - slope form
The equation (y - y_1=m(x - x_1)) is the point - slope form of a line, where ((x_1,y_1)) is a point on the line and (m) is the slope. For the equation (y - 6=-4(x+2)) (which can be rewritten as (y - 6=-4(x-(-2)))), we have (x_1=-2), (y_1 = 6) and (m=-4). So, one point on the line is ((-2,6)) and the slope (m=-4=\frac{-4}{1}).
Step2: Plot the initial point
Plot the point ((-2,6)) on the coordinate plane.
Step3: Use the slope to find another point
The slope (m=\frac{\text{rise}}{\text{run}}=-4=\frac{-4}{1}). From the point ((-2,6)):
- Move 1 unit to the right (run = 1) and 4 units down (rise=-4). The new point is ((-2 + 1,6-4)=( - 1,2)).
Step4: Draw the line
Connect the points ((-2,6)) and ((-1,2)) with a straight line. Extend the line in both directions to complete the graph of the line (y - 6=-4(x + 2)).