Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
*answer is to be written as f(x)=
![The task is to find a formula for the linear function depicted in the graph.
### Graph Description:
- **Axes**:
- The horizontal axis is labeled as \(x\), ranging from -10 to 10.
- The vertical axis is labeled as \(y\), also ranging from -10 to 10.
- **Grid**:
- The graph is shown on a grid with intervals marked at each integer value, providing precise plotting of points.
- **Line**:
- The graph contains a straight line passing through the coordinate axes.
- The line intersects the y-axis at \(-10\) and the x-axis at \(5\).
### Explanation:
To determine the equation of the line, we need to find the slope \(m\) and the y-intercept \(b\) for the line equation in the slope-intercept form:
\[
y = mx + b
\]
- **Y-intercept (\(b\))**: The line crosses the y-axis at \(-10\), so \(b = -10\).
- **Slope (\(m\))**: The slope is the change in \(y\) divided by the change in \(x\) between two points on the line.
- Using the intercepts, the change in \(y\) from \(-10\) to \(0\) (y-intercept to the line crossing x-axis) is \(10\).
- The change in \(x\) from \(0\) to \(5\) (y-intercept to the line crossing x-axis) is \(5\).
Thus, the slope \(m\) is:
\[
m = \frac{10}{5} = 2
\]
- **Equation**: Substituting the slope and y-intercept into the equation:
\[
y = 2x - 10
\]
This is the formula for the linear function depicted by the graph.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdad9db74-a689-4374-b398-94285063bb6c%2F80d0f9b3-cac3-48b0-b41c-22456c8daacc%2Fgxht6jf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The task is to find a formula for the linear function depicted in the graph.
### Graph Description:
- **Axes**:
- The horizontal axis is labeled as \(x\), ranging from -10 to 10.
- The vertical axis is labeled as \(y\), also ranging from -10 to 10.
- **Grid**:
- The graph is shown on a grid with intervals marked at each integer value, providing precise plotting of points.
- **Line**:
- The graph contains a straight line passing through the coordinate axes.
- The line intersects the y-axis at \(-10\) and the x-axis at \(5\).
### Explanation:
To determine the equation of the line, we need to find the slope \(m\) and the y-intercept \(b\) for the line equation in the slope-intercept form:
\[
y = mx + b
\]
- **Y-intercept (\(b\))**: The line crosses the y-axis at \(-10\), so \(b = -10\).
- **Slope (\(m\))**: The slope is the change in \(y\) divided by the change in \(x\) between two points on the line.
- Using the intercepts, the change in \(y\) from \(-10\) to \(0\) (y-intercept to the line crossing x-axis) is \(10\).
- The change in \(x\) from \(0\) to \(5\) (y-intercept to the line crossing x-axis) is \(5\).
Thus, the slope \(m\) is:
\[
m = \frac{10}{5} = 2
\]
- **Equation**: Substituting the slope and y-intercept into the equation:
\[
y = 2x - 10
\]
This is the formula for the linear function depicted by the graph.
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