Question

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

Explanation:

Step1: Identify the form

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

Step2: Plot the point

Plot the point \( (-5,-2) \) on the coordinate plane.

Step3: Use the slope

The slope \( m = -\frac{1}{2} \) means for every 2 units we move to the right (increase in \( x \) by 2), we move down 1 unit (decrease in \( y \) by 1). From the point \( (-5,-2) \), moving 2 units right (to \( x=-5 + 2=-3 \)) and 1 unit down (to \( y=-2-1 = - 3 \)) gives the point \( (-3,-3) \). We can also move 2 units left (to \( x=-5-2=-7 \)) and 1 unit up (to \( y=-2 + 1=-1 \)) to get the point \( (-7,-1) \).

Step4: Draw the line

Draw a straight line passing through the plotted points.

Answer:

To graph the line \( y + 2=-\frac{1}{2}(x + 5) \), plot the point \((-5,-2)\) and then use the slope \( -\frac{1}{2} \) to find other points (e.g., \((-3,-3)\) and \((-7,-1)\)) and draw a line through them.