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Chapter 11: Problem 129

In the following exercises, find the intercepts. $$ x+y=-2 $$

Short Answer

Expert verified
The x-intercept is (-2, 0) and the y-intercept is (0, -2).

Step by step solution

01

Finding the x-intercept

To find the x-intercept, set the value of y to 0. Plugging in y=0 into the equation, we get:\[ x + 0 = -2 \]Solving for x, we find:\[ x = -2 \]Thus, the x-intercept is (-2, 0).
02

Finding the y-intercept

To find the y-intercept, set the value of x to 0. Plugging in x=0 into the equation, we get:\[ 0 + y = -2 \]Solving for y, we find:\[ y = -2 \]Thus, the y-intercept is (0, -2).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

x-intercept
The x-intercept of a line is the point where the line crosses the x-axis. This means that the y-value at this point is zero. To find the x-intercept, you set y to 0 in the equation of the line and solve for x.
In our exercise, the equation is:
\( x + y = -2 \)
To find the x-intercept:
1. Set y to 0.
2. Substitute y=0 in the equation, which gives us: \( x + 0 = -2 \)
3. Solve for x: \( x = -2 \)
So, the x-intercept is (-2, 0). This point represents where the line will cross the x-axis.
y-intercept
The y-intercept of a line is the point where the line crosses the y-axis. This point has an x-value of zero. To find the y-intercept, you set x to 0 in the equation of the line and solve for y.
For our exercise, the equation is:
\( x + y = -2 \)
To find the y-intercept:
1. Set x to 0.
2. Substitute x=0 in the equation, which gives us: \( 0 + y = -2 \)
3. Solve for y: \( y = -2 \)
Thus, the y-intercept is (0, -2). This point represents where the line will cross the y-axis.
solving linear equations
Solving linear equations involves finding the values of variables that make the equation true. When dealing with a linear equation like \( x + y = -2 \), we often solve for one variable at a time.
There are a few steps you should always follow:
  • Identify what's given and what you need to find.
  • Isolate the variable by using basic arithmetic operations like addition, subtraction, multiplication, or division.
  • Substitute known values to solve for the unknown variable.
For example:
1. If we need to find the x-intercept, we set y to 0, then solve for x, giving us x = -2.
2. If we need to find the y-intercept, we set x to 0, then solve for y, yielding y = -2.
This method is useful for finding points where the line crosses the axes and gives us critical information about the graph of the line.

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