Question

graph the line.
x + y = -3

Explanation:

Step1: Rewrite in slope - intercept form

We start with the equation \(x + y=-3\). To get it in the form \(y = mx + b\) (where \(m\) is the slope and \(b\) is the y - intercept), we solve for \(y\). Subtract \(x\) from both sides of the equation: \(y=-x - 3\). Here, the slope \(m=- 1\) and the y - intercept \(b = - 3\).

Step2: Find the y - intercept point

The y - intercept is the point where the line crosses the y - axis. When \(x = 0\), we substitute into \(y=-x - 3\). So \(y=-0 - 3=-3\). So one point on the line is \((0,-3)\).

Step3: Use the slope to find another point

The slope \(m=-1=\frac{-1}{1}=\frac{\text{rise}}{\text{run}}\). From the point \((0,-3)\), if we move 1 unit to the right (run = 1) and 1 unit down (rise=-1), we get the point \((0 + 1,-3-1)=(1,-4)\). Alternatively, if we move 1 unit to the left (run=-1) and 1 unit up (rise = 1), we get the point \((0-1,-3 + 1)=(-1,-2)\).

Step4: Plot the points and draw the line

Plot the points \((0,-3)\) and, for example, \((1,-4)\) (or any other point found using the slope) on the coordinate plane. Then draw a straight line through these points.

(Note: Since the problem is about graphing, the final answer is the graph of the line \(y=-x - 3\) with a y - intercept at \((0,-3)\) and a slope of - 1. The process above describes how to obtain the graph.)

Answer:

The graph of the line \(x + y=-3\) (or \(y=-x - 3\)) has a y - intercept at \((0, - 3)\) and a slope of \(-1\). It passes through points like \((0,-3)\), \((1,-4)\), \((-1,-2)\) etc. and is a straight line drawn through these points on the coordinate plane.