Question

x + y = -1
y = -x - 1
click to select points on the graph.

Explanation:

Step1: Rewrite the equations in slope - intercept form

For the equation \(x + y=- 1\), we can rewrite it as \(y=-x - 1\) (by subtracting \(x\) from both sides of the equation \(x + y=-1\)). So both equations \(x + y=-1\) and \(y=-x - 1\) are the same linear equation.
The slope - intercept form of a linear equation is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For \(y=-x - 1\), the slope \(m=-1\) and the y - intercept \(b = - 1\).

Step2: Find the y - intercept point

The y - intercept occurs when \(x = 0\). Substitute \(x = 0\) into \(y=-x - 1\), we get \(y=-0 - 1=-1\). So one point on the line is \((0,-1)\).

Step3: Find another point using the slope

The slope \(m=-1=\frac{-1}{1}\), which means for a run (change in \(x\)) of \(1\), the rise (change in \(y\)) is \(- 1\). Starting from the point \((0,-1)\), if we increase \(x\) by \(1\) (i.e., \(x = 0+1 = 1\)), then \(y=-1+( - 1)=-2\). So another point is \((1,-2)\).
We can also find the x - intercept. The x - intercept occurs when \(y = 0\). Substitute \(y = 0\) into \(y=-x - 1\), we have \(0=-x - 1\), then \(x=-1\). So the point \((-1,0)\) is also on the line.

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

• Plot the point \((0,-1)\) (the y - intercept).
• Plot the point \((-1,0)\) (the x - intercept) or \((1,-2)\) (using the slope from \((0,-1)\)).
• Draw a straight line through these points.

Answer:

To graph \(y=-x - 1\) (equivalent to \(x + y=-1\)):

• Plot the point \((0,-1)\) (since when \(x = 0\), \(y=-1\)).
• Plot the point \((-1,0)\) (since when \(y = 0\), \(x=-1\)).
• Draw a straight line passing through these two points (and other points like \((1,-2)\) can also be used for accuracy).