Mathematics
Grade 11
15 min
Find the slope of a linear function
Find the slope of a linear function
What you'll learn
- Identify the start time and end time on an analog clock with accuracy.
- Solve word problems involving elapsed time in 5-minute intervals using a number line or clock model to find the answer with 80% accuracy.
- Explain how to calculate elapsed time by counting forward from the start time to the end time in minutes.
- Apply the concept of elapsed time to real-world scenarios, such as determining the length of a TV show or the duration of playtime, with 75% accuracy.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Calculate the slope of a linear function given two distinct points.
Determine the slope of a linear function from its graph by analyzing 'rise over run'.
Identify the slope of a linear function when its equation is presented in slope-intercept form (f(x) = mx + b).
Algebraically manipulate a linear equation from standard form (Ax + By = C) to find its slope.
Interpret the slope as a rate of change in a real-world context.
Differentiate between positive, negative, zero, and undefined slopes and describe the corresponding line's orientation.
Have you ever wondered how engineers determine the steepness of a road or how economists track profit growth over time? 📈 They're all using the concept of slope!
This tutorial will provide a deep d...
2
Key Concepts & Vocabulary
TermDefinitionExample
Linear FunctionA function that can be represented by an equation of the form f(x) = mx + b. Its graph is a straight line.f(x) = 2x - 3 is a linear function. For every one-unit increase in x, the value of f(x) increases by two units.
Slope (m)A measure of the steepness and direction of a line. It is defined as the ratio of the vertical change (rise) to the horizontal change (run) between any two distinct points on the line.A slope of 3 means that for every 1 unit you move to the right on the x-axis, you must move 3 units up on the y-axis.
Rate of ChangeDescribes how one quantity changes in relation to another quantity. For a linear function, the rate of change is constant and is equal to the slope.If a car travels at a constant 60 km/h, its rate of change of distance...
3
Core Formulas
The Slope Formula
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{\Delta y}{\Delta x}
Use this formula when you are given the coordinates of two points (x₁, y₁) and (x₂, y₂) on a line. Ensure that the order of subtraction is consistent for both the numerator and the denominator.
Slope-Intercept Form
f(x) = mx + b \quad \text{or} \quad y = mx + b
When a linear function is written in this form, the slope is the coefficient 'm' of the x-term. The 'b' represents the y-intercept, the point where the line crosses the y-axis.
Slope from Standard Form
\text{For an equation } Ax + By = C, \text{ the slope is } m = -\frac{A}{B} \quad (\text{where } B \neq 0)
This is a shortcut to find the slope when a linear equation is in standard form. Alternatively, you can alge...
4 more steps in this tutorial
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Sign Up Free to ContinueSample Practice Questions
Easy
In the linear function f(x) = -5x + 12, what is the slope of the line?
A.12
B.-5
C.5
D.x
Easy
Which of the following correctly defines the slope 'm' of a line passing through two distinct points (x₁, y₁) and (x₂, y₂)?
A.m = (x₂ - x₁) / (y₂ - y₁)
B.m = (y₂ + y₁) / (x₂ + x₁)
C.m = (y₂ - y₁) / (x₂ - x₁)
D.m = (x₁ - y₁) / (x₂ - y₂)
Easy
A horizontal line has a slope that is...
A.Positive
B.Negative
C.Undefined
D.Zero
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What grade level is "Find the slope of a linear function"?
Find the slope of a linear function is a Grade 11 Mathematics lesson on ExcelOS.
What will I learn in Find the slope of a linear function?
You'll be able to: Identify the start time and end time on an analog clock with accuracy; Solve word problems involving elapsed time in 5-minute intervals using a number line or clock model to find the answer with 80% accuracy; Explain how to….
Is "Find the slope of a linear function" free to practice?
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How many practice questions are included with Find the slope of a linear function?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.