Problem 305 In the following exercises, find... [FREE SOLUTION]

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Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2016 Edition

Chapter 11: Problem 305

In the following exercises, find the intercepts. $$ x-y=-1 $$

Short Answer

Expert verified

x-intercept: (-1, 0), y-intercept: (0, 1)

Step by step solution

Find the x-intercept

To find the x-intercept, set y to 0 in the equation and solve for x:\[x - y = -1\]Substitute y = 0:\[x - 0 = -1\]So:\[x = -1\]Therefore, the x-intercept is (-1, 0).

Find the y-intercept

To find the y-intercept, set x to 0 in the equation and solve for y:\[x - y = -1\]Substitute x = 0:\[0 - y = -1\]So:\[-y = -1\]Solve for y:\[y = 1\]Therefore, the y-intercept is (0, 1).

Summarize the intercepts

The calculated intercepts are:x-intercept: (-1, 0)y-intercept: (0, 1)

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Key Concepts

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

x-intercept

To find the x-intercept of a linear equation, you need to set the value of y to zero and solve for x. This is because the x-intercept is where the graph of the equation crosses the x-axis, and all points on the x-axis have a y-coordinate of zero.

Let's look at an example using the equation:
x - y = -1
First, set y to 0 and solve for x: x = -1
This tells us the x-intercept is at the point (-1, 0).

Finding the x-intercept is straightforward:

Set y to 0 in the equation.
Solve the equation for x.

Remember, the x-intercept is always expressed as a point (x, 0).

y-intercept

To find the y-intercept, set the value of x to zero and solve for y. The y-intercept is where the graph crosses the y-axis, and all points on the y-axis have an x-coordinate of zero.

Using the same example: x - y = -1

Set x to 0 and solve for y: -y = -1
So, y = 1
Therefore, the y-intercept is at the point (0, 1).

Here's the process in simpler terms:

Set x to 0 in the equation.
Solve the equation for y.

The y-intercept is always written as a point (0, y). It's just as easy to find as the x-intercept.

linear equations

Linear equations are equations of the first degree, meaning they will graph as straight lines on a coordinate plane. The general form of a linear equation is Ax + By = C, where A, B, and C are constants.

In our example, x - y = -1 is a linear equation.

Linear equations have unique features:

They graph as straight lines.
They have both x-intercepts and y-intercepts.
Their solutions are any pair (x, y) that make the equation true.

Intercepts offer a quick way to understand the graph of a linear equation. Knowing how to find these intercepts can help you draw the line accurately. Plus, understanding these points is crucial for solving and graphing more complex equations later on.

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91影视

In the following exercises, find the intercepts. $$ x-y=-1 $$

Short Answer

Step by step solution

Find the x-intercept

Find the y-intercept

Summarize the intercepts

Key Concepts

x-intercept

y-intercept

linear equations

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