# WEEK 15-LINEAR-FUNCTIONS-IN-SLOPE-INTERCEPT-FORM

VIMSCHOOL

Created on September 10, 2024

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## Transcript

Objectives

Start

Linear Functions in Slope-Intercept Form

1

2

Linear Function Equation

Parts of Linear Functions

Applied Problems

Summary

Graphing Linear Functions

Linear Function Equation

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The Slope-Intercept Form

Definition: A linear equation in the slope-intercept form is:

Where:

is called the slope

is called the intercept

m

b

y=mx+b

Example 1: is a linear function where:

y=x-6

Slope: m=1

Intercept:b=-6

Parts of Linear Functions

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The Slope m.

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 the line, the slope is computed as follows:

Change of x

Change of y

The intercept b.

Definition: The intercept b is the y coordinate at which the line intercepts with the y-axis.

Let's see some examples:

Example 1: A line passes through points (1,2) and (3,6). Find the line equation.

y=2x

Step 3

Step 2

Step 1

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Step 0: (Optative) Plot the two points and trace a line passing through them.

Replace in the general form of the equation the values of m and b found.

Find the intercept replacing the values of m and one of the given points.

Find the slope of the line.

1

Interpreting Key Features of Linear Equations

Slope

intercepts

Values of Definition

X-INTERCEPT

2

Y-INTERCEPT

Rate of change of a linear equation

DOMAIN

RANGE

3

X-intercept Occurs when y=0

Y-intercept=b Occurs when x=0

Domain=Inputs All possible values that can be replaced for x.

Domain=Outputs All possible values that can be replaced for y.

Graphing Linear Functions

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Let's see some examples:

Example 1: Graph doing a table of values.

y=2x-3

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1. Select two values of x and put them in a table.

2. Calculate values of y for each value of x: y=2(0)-3=-3 y=2(1)-3=-1

3. Place points on a Cartesian plane.

4. Join points with a straight line extending to left and to the right of both points.

Try it by yourself:

Applied Problems

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Speed is proportional

If a car travels 30 kilometers per hour, starting at 10km from the center of the city.

Solution

a) Identify givens. b) Find the line equation describing the motion. c) Plot the line equation found.

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07:00

Try it by Yourself

The table below shows the number of hours worked (x) and the amount earned (y).

a) Plot the points on a Cartesian Plane. b) Find the linear equation that represents the relationship between hours worked and earnings.

Click to see the data.

🤔

🤔

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SLOPE

INTERCEPTS

VALUES OF DEFINITION

Y-INTERCEPT

Rate of change of a line

X-INTERCEPT

RANGE

DOMAIN

Summary:Features of Lines

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Welcome 6th graders!

A journey soon begin through Social Science experiences!

Great job!

See you next time

8TH-LINEAR-FUNCTIONS-IN-SLOPE-INTERCEPT-FORM-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.3.3 Given a table, graph or written description of a linear relationship, write an equation in slope-intercept form.MA.K12.MTR.2.1 "Demonstrate understanding by representing problems in multipleways."ELA.K12.EE.2.1 Read and comprehend grade-level complex texts proficiently.

Solution

Step 3

Step 2

b) y=15x

Step 1

Answer

Step 4

a)

b)

1. Plot points on a Cartesian Plane.

2. Find the slope.

4. Replace all of the values found in line equation.

3. Find the intercept.

Solution

Step 3

Step 2

Step 1

Answer

b)

a)

b) d=30t+10

c)

d: distance (kilometers) t: time (hours)

d=30t+10

1. Unit rate is the increment (raise) given in the information. Instead of m, we use v for speed.

2. Use equation y=mx+b. Here y->d x->t

4. Place points of the table in a Cartesian plane.

4. Join points with a straight line.