Question

graph this line:
y - 2 = -4(x - 1)
click to select points on the graph.
submit
work it out
not feeling ready yet? these can help:
graph a line using slope (0)
lesson: point - slope form

Explanation:

Step1: Identify the point and slope

The equation is in point - slope form \(y - y_1=m(x - x_1)\), where \((x_1,y_1)=(1,2)\) and \(m = - 4\).

Step2: Plot the point \((1,2)\)

Locate the point with \(x = 1\) and \(y=2\) on the coordinate plane.

Step3: Use the slope to find another point

The slope \(m=-4=\frac{-4}{1}\). From the point \((1,2)\), move down 4 units (because the numerator of the slope is - 4, which represents a change in \(y\)) and then move right 1 unit (because the denominator of the slope is 1, which represents a change in \(x\)). This gives the point \((1 + 1,2-4)=(2,-2)\). We can also move up 4 units and left 1 unit from \((1,2)\) to get \((1-1,2 + 4)=(0,6)\).

Step4: Draw the line

Connect the points (for example, \((1,2)\), \((2,-2)\), and \((0,6)\)) with a straight line.

Answer:

To graph the line \(y - 2=-4(x - 1)\):

1. Plot the point \((1,2)\) (from the point - slope form \(y - y_1=m(x - x_1)\) where \(x_1 = 1,y_1=2\)).
2. Use the slope \(m=-4\) (rise/run=\(-4/1\)):

• From \((1,2)\), move down 4 units and right 1 unit to get \((2,-2)\), or move up 4 units and left 1 unit to get \((0,6)\).

1. Draw a straight line through the plotted points.