# WEEK 14-SLOPE-OF-LINEAR-FUNCTIONS

VIMSCHOOL

Created on September 10, 2024

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## Transcript

Objectives

Start

Slope of Linear Functions

1

2

Story

What is Slope?

Classification of Slopes

Summary

Finding Slope

Story

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What is Slope?

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🗨️

Before getting started, let's see how to find the change of a variable from a graph or table.

1

🗨️

Suppose that a car starts moving from 10m of the cross walk to 60m.

2

Someone takes time in a stopwatch. Time measured is 20 seconds.

Let's find the changes in position and time.

Change of time=|20s-0s|=20s

Change of distance=|60m-10m|=50m

1

In the previous example we saw that changes are given by differences between initial and final values.

That is: Change of a variable where x₂: Final value x₁: Initial Value.

= x₂-x₁,

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The Slope Calculation.

Definition: The slope is the rate of change of y (dependent variable) when x is changed.

If (x₁,y₁), (x₂,y₂) are two points on a line, the slope is computed as follows:

Change of x

Change of y

Let's see some examples:

Example 1: Find the slope of the line passing through points (1,2), (3,5)

Example 2: Find the slope of the line passing through (0,6) and (2,2)

m=-2

m=1

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1. Identify in a graph: 1st point: (x1, y1) = (1,2) 2nd point: (x2, y2) = (3,4)

2. Replace values into slope's formula:

3. Subtract values.

4. Divide numerator and denominator.

Finding Slope from Graphs and Tables

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Let's see some examples:

Example 1: Find the slope of the line shown in the graph below.

Example 2: Find the slope in the table shown. What's the meaning of the slope?

Each additional apple costs $9

m=9

m=-

3 4

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Problem might be solved drawing the total (light orange) and subtracting the additional (10).

1.

2.

Classification of Slopes

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1

Interpreting Key Features of Linear Equations

Positive slope

negative slope

Zero slope

m<0

m>0

2

m=0

3

Increasing function/Line upwards. m=+1

Decreasing function/ Line downwards. m=-3/4

Horizontal Line m=0:

Meaning For each increase (run) of x, y increases (raises) m units. Example: m=+1, m=+2,...

Meaning For each increase (run) of x, y decreases m units. Example: m=-1, m=-2,...

Meaning For each increase (run) of x, y does not change. Example: m=0

Let's see some examples:

Example 1: Classificate the function according to the slope.

Example 2: For the situation discussed on , find the slope and interpret their meaning

m=2.5

page 6

Decreasing function

f(x) = -4x+2

Slope is the term accompanying the variable.

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1.

4. The slope is the velocity and is +, so it moves to the right or upwards (direction of +x axis)

02:30

Try it by yourself:

( , )

( , )

and

( , )

( , )

and

( , )

( , )

and

->

->

->

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Try it by yourself:

Rate of change of a line

Given graph?

Given pointstable?

Summary:Slope

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Given (x1,y1), (x2,y2) use definition formula: m= y2-y1 x2-x1

Look up one point in the graph and see how y raises after raising x one unit.

Welcome 6th graders!

A journey soon begin through Social Science experiences!

Great job!

See you next time

8TH-SLOPE-OF-LINEAR-FUNCTIONS-EN © 2024 by CASURID is licensed under CC BY-NC-ND 4.0

It is highly advised to have:

MATERIAL

- Grid paper.
- Pencils of different colors.
- Eraser.
- A rule.
- A compass.
- A Protactor.
- A calculator.
- Geogebra installed on your phone/tablet/computer (or use online version).

"MA.8.AR.3 Extend understanding of proportional relationships to two- variable linear equations." MA.8.AR.3.2 Given a table, graph or written description of a linear relationship, determine the slope. ELA.K12.EE.1.1 Cite evidence to explain and justify reasoning.