Question

graph the line using the information provided.

1. $y + 2 = 2(x - 1)$

Explanation:

Step1: Identify the form

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

Step2: Plot the point

Locate the point \( (1,-2) \) on the coordinate plane.

Step3: Use the slope

The slope \( m = 2=\frac{2}{1} \), which means from the point \( (1,-2) \), we can move up 2 units and right 1 unit to get another point \( (1 + 1,-2+2)=(2,0) \), or down 2 units and left 1 unit to get \( (1 - 1,-2 - 2)=(0,-4) \).

Step4: Draw the line

Draw a straight line through the plotted points (e.g., \( (1,-2) \), \( (2,0) \), \( (0,-4) \)) to represent the line \( y + 2 = 2(x - 1) \).

Answer:

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

1. Identify the point from point - slope form: The line passes through \( (1,-2) \) with a slope of 2.
2. Plot the point \( (1,-2) \).
3. Use the slope (rise 2, run 1) to find additional points (e.g., \( (2,0) \), \( (0,-4) \)).
4. Draw a straight line through these points.