Problem 157 Find the intercepts for each equ... [FREE SOLUTION]

Chapter 4: Problem 157

Find the intercepts for each equation. \(x-y=-3\)

Short Answer

Expert verified

x-intercept: (-3, 0); y-intercept: (0, 3)

Step by step solution

Find the x-intercept

To find the x-intercept, set y to 0 and solve for x. The equation becomes: \[ x - 0 = -3 \] So, \[ x = -3 \] Therefore, the x-intercept is (-3, 0).

Find the y-intercept

To find the y-intercept, set x to 0 and solve for y. The equation becomes: \[ 0 - y = -3 \] So, \[ -y = -3 \] which simplifies to \[ y = 3 \] Therefore, the y-intercept is (0, 3).

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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 is the point where the graph of an equation crosses the x-axis. This happens when the value of y is 0. To find the x-intercept, you set y to 0 and solve for x in the given equation.

For example, consider the equation: \(x - y = -3\). To find the x-intercept, set \(y = 0\). The equation then becomes: \[ x - 0 = -3 \]
Solving this gives:
\[ x = -3 \]
Therefore, the x-intercept is \(-3, 0\).

In summary, always remember these steps to find the x-intercept:

Set \(y\) to 0
Solve for \(x\)

y-intercept

The y-intercept is where the graph crosses the y-axis. This occurs when the value of x is 0. To find the y-intercept, set x to 0 in the given equation and solve for y.

For example, with the equation: \(x - y = -3\), to find the y-intercept, set \(x = 0\). The equation becomes: \[ 0 - y = -3 \]
Solving this gives:
\[ -y = -3 \] which simplifies to
\[ y = 3 \] Therefore, the y-intercept is \(0, 3\).

To summarize the steps to find the y-intercept:

Set \(x\) to 0
Solve for \(y\)

solving equations

Solving equations involves finding the value of the variable that makes the equation true. There are various methods to solve equations, but the basic aim is to isolate the variable on one side of the equation.

Let's consider the example equation: \(x - y = -3\). To find the intercepts, follow these steps:

Isolate the variable in question by performing inverse operations. For the x-intercept, isolate x by setting \(y = 0\) and for the y-intercept, isolate y by setting \(x = 0\).
Make sure to perform the same operation on both sides of the equation to maintain the equality.
Simplify the equation to solve for the variable.

By following these steps, you can confidently solve for x and y intercepts and understand how to navigate through linear equations. This understanding is essential in various applications such as graphing linear equations and analyzing their behavior.

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91影视

Find the intercepts for each equation. \(x-y=-3\)

Short Answer

Step by step solution

Find the x-intercept

Find the y-intercept

Key Concepts

x-intercept

y-intercept

solving equations

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