Question

graph the line.
$y + 3 = -\dfrac{1}{3}(x + 5)$

Explanation:

Step1: Identify the form

The equation \( y + 3 = -\frac{1}{3}(x + 5) \) is in point - slope form \( y - y_1=m(x - x_1) \), where \( (x_1,y_1)=(-5,-3) \) and \( m =-\frac{1}{3} \).

Step2: Plot the point

First, plot the point \( (-5,-3) \) on the coordinate plane.

Step3: Use the slope

The slope \( m =-\frac{1}{3} \) means for every 3 units we move to the right (increase in \( x \) by 3), we move down 1 unit (decrease in \( y \) by 1). From the point \( (-5,-3) \), moving 3 units to the right (to \( x=-5 + 3=-2 \)) and 1 unit down (to \( y=-3-1=-4 \)) gives the point \( (-2,-4) \). We can also move 3 units to the left ( \( x=-5 - 3=-8 \)) and 1 unit up ( \( y=-3 + 1=-2 \)) to get the point \( (-8,-2) \).

Step4: Draw the line

Draw a straight line passing through the plotted points.

Answer:

The line is graphed by first plotting the point \((-5, - 3)\) and then using the slope \(-\frac{1}{3}\) to find additional points (e.g., \((-2, - 4)\) and \((-8, - 2)\)) and drawing a straight line through them.