Question

graph this line:
$y - 5 = \frac{1}{2}(x + 1)$

Explanation:

Step1: Identify the form

The equation \( y - 5=\frac{1}{2}(x + 1) \) is in point - slope form \( y - y_1=m(x - x_1) \), where \( m \) is the slope and \( (x_1,y_1) \) is a point on the line. Here, \( m=\frac{1}{2} \) and the point is \( (- 1,5) \) (since \( y_1 = 5 \) and \( x_1=-1 \) as \( x - (-1)=x + 1 \)).

Step2: Plot the point

First, plot the point \( (-1,5) \) on the coordinate plane.

Step3: Use the slope to find another point

The slope \( m=\frac{1}{2}=\frac{\text{rise}}{\text{run}} \). From the point \( (-1,5) \), we move up 1 unit (rise) and then move to the right 2 units (run). So the new point will be \( (-1 + 2,5+1)=(1,6) \). We can also move down 1 unit and left 2 units from \( (-1,5) \) to get another point \( (-1-2,5 - 1)=(-3,4) \).

Step4: Draw the line

Draw a straight line passing through the plotted points (e.g., \( (-1,5) \), \( (1,6) \), \( (-3,4) \)).

Answer:

To graph the line \( y - 5=\frac{1}{2}(x + 1) \), plot the point \( (-1,5) \), then use the slope \( \frac{1}{2} \) to find other points (e.g., \( (1,6) \) by moving up 1 and right 2 from \( (-1,5) \)) and draw a straight line through them.