Linear Relationships and Equations

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to Lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the slope of a line that rises from left to right?

  • Negative
  • Undefined
  • Zero
  • Positive (correct)

A horizontal line has a positive slope.

False (B)

What is the formula for finding the slope given two points, (x₁, y₁) and (x₂, y₂)?

m = (y₂ - y₁) / (x₂ - x₁)

In the slope-intercept form, y = mx + b, 'b' represents the ______.

<p>y-intercept</p> Signup and view all the answers

Match the forms of linear equations with their definitions:

<p>Slope-intercept form = y = mx + b Point-slope form = y - y₁ = m(x - x₁) Standard form = Ax + By = C Slope formula = m = (y₂ - y₁) / (x₂ - x₁)</p> Signup and view all the answers

To solve the equation 3x + 5 = 20, what is the first step?

<p>Subtract 5 from both sides (C)</p> Signup and view all the answers

In a linear equation, the highest power of the variable is 2.

<p>False (B)</p> Signup and view all the answers

What do you call a line that has an undefined slope?

<p>Vertical line</p> Signup and view all the answers

If a line passes through points (2, 3) and (4, 7), the slope is ______.

<p>2</p> Signup and view all the answers

Which form should be used to write an equation if you have the slope and a point?

<p>Point-slope form (C)</p> Signup and view all the answers

Flashcards

Line

A straight path that extends infinitely in both directions.

Rate of change

The amount a quantity changes over time or in relation to another quantity.

Linear relationship

A relationship where the rate of change is constant, meaning the line representing it is straight.

Slope

The steepness of a line, calculated by dividing the vertical change (rise) by the horizontal change (run).

Signup and view all the flashcards

Positive slope

A line that slopes upwards from left to right.

Signup and view all the flashcards

Negative slope

A line that slopes downwards from left to right.

Signup and view all the flashcards

Zero slope

A horizontal line with no vertical change, thus a slope of 0.

Signup and view all the flashcards

Undefined slope

A vertical line with no horizontal change, resulting in undefined slope.

Signup and view all the flashcards

Slope-intercept form

An equation that can be written in the form y = mx + b, where 'm' is the slope and 'b' is the y-intercept.

Signup and view all the flashcards

Point-slope form

An equation that can be written in the form y - y₁ = m(x - x₁), where 'm' is the slope and (x₁, y₁) is a point on the line.

Signup and view all the flashcards

Study Notes

Lines and Linear Relationships

  • Lines are straight paths that extend indefinitely in both directions.
  • Rate of change describes how much a quantity changes over time or relative to another quantity. In a linear relationship, the rate of change is constant.
  • Slope measures the steepness of a line. It is calculated as the vertical change (rise) divided by the horizontal change (run).
    • Positive slope: line rises from left to right.
    • Negative slope: line falls from left to right.
    • Zero slope: horizontal line.
    • Undefined slope: vertical line.

Creating and Solving Linear Relations

  • A linear relation can be expressed in various forms, including:
    • Slope-intercept form: y = mx + b, where 'm' is the slope and 'b' is the y-intercept (the point where the line crosses the y-axis).
    • Point-slope form: y - y₁ = m(x - x₁), where 'm' is the slope and (x₁, y₁) is a point on the line.

Finding the Equation of a Line

  • From the slope and a point: Use the point-slope form.
  • From two points: Use the slope formula first, then the point-slope form.

Solving Linear Equations

  • Linear equations involve variables to the first power.
    • To solve, isolate the variable using inverse operations.
  • Example methods include:
    • Combining like terms
    • Using the distributive property
    • Adding or subtracting to both sides of the equation
    • Multiplying or dividing to both sides of the equation

Creating Linear Equations

  • Given specific conditions, like slope and a point or two points, use the appropriate forms of the linear equation to derive the equation for the line.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Quiz Team

More Like This

Use Quizgecko on...
Browser
Browser