What is the general form of a linear equation with one independent variable?

$y=a+bx$, where $a$ and $b$ are constants, $x$ is independent, and $y$ depends on $x$.

What does the slope $b$ represent?

It represents the constant change in $y$ for each one-unit increase in $x$, and determines the line's direction and steepness.

What does the y-intercept $a$ represent?

It is the value of $y$ when $x=0$; the graph crosses the y-axis at $(0,a)$.

How can you graph a linear equation?

Substitute several values of $x$ to find corresponding $y$ values, plot the resulting ordered pairs, and draw the straight line through them.

What are the slope and intercept in $C=31.50+32h$?

The slope is $32$ dollars per hour, the added cost for each hour. The intercept is $31.50$, the one-time fixed charge.

Business statisticsLesson 1 of 2 in the course Linear Regression and Correlation

Linear Equations: Slope, Intercepts, and Business Models

5 flashcards · 5 quiz questions · 5 match pairs · 4 fill-in sentences · English

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Summary

Linear equations describe relationships between two variables using a straight line. In this lesson, you will learn how to interpret the equation $y=a+bx$ , identify its independent and dependent variables, understand slope and the y-intercept, and use the equation to model real-world costs and earnings.

Here, $a$ and $b$ are constants. The variable $x$ is the independent variable: its value is chosen or observed. The variable $y$ is the dependent variable: its value is determined by the equation and depends on $x$ .

All flashcards

What is the general form of a linear equation with one independent variable?: $y=a+bx$ , where $a$ and $b$ are constants, $x$ is independent, and $y$ depends on $x$ .
What does the slope $b$ represent?: It represents the constant change in $y$ for each one-unit increase in $x$ , and determines the line's direction and steepness.
What does the y-intercept $a$ represent?: It is the value of $y$ when $x=0$ ; the graph crosses the y-axis at $(0,a)$ .
How can you graph a linear equation?: Substitute several values of $x$ to find corresponding $y$ values, plot the resulting ordered pairs, and draw the straight line through them.
What are the slope and intercept in $C=31.50+32h$ ?: The slope is $32$ dollars per hour, the added cost for each hour. The intercept is $31.50$ , the one-time fixed charge.

Quiz questions

Which symbol denotes the dependent variable in $y=a+bx$ ?Answer: $y$
In the equation $y=7+4x$ , what is the slope?Answer: $4$
Where does the graph of $y=-1+2x$ cross the y-axis?Answer: At $(0,-1)$
A service charges a $20 fixed fee plus $12 per hour. Which equation gives total cost $C$ for $h$ hours?Answer: $C=20+12h$
Does a linear equation relating two variables by itself prove that one variable causes changes in the other?Answer: No; the equation alone does not establish causation.

Based on Introductory Business Statistics 2e by Alexander Holmes, Barbara Illowsky, Susan Dean (OpenStax), licensed CC BY 4.0. Adapted into a summary, flashcards and quizzes.

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