Linear functions

Did you realise Book Creator could be used in the mathematics classroom? It can! Here are some great examples.

Math books

Narrow ruled paper

Writing linear equations in slope-intercept form when given..... A graph

There are many ways to write a linear equation. You have to learn to write linear equations in slope-intercept form. 	In this chapter, you will learn the different ways you need to know in order to put a linear equation in slope-intercept form.

When given a graph you need to find the y-intercept (where the line crosses the y-axis) then find the slope (the rate of change in a line) and plug it into the formula (y = mx+b)

To find and put an equation into slope-intercept form when given a graph all you need to do is.... 1. Find the y-intercept 2. Find the slope 3. Input the information into the equation (y=mx+b)

Marble

Writing linear equations in slope-intercept form when given..... The Slope and Y-intercept

Sometimes you may encounter an equation in standard form. You might have to change it into slope-intercept form in order to solve it. 	In this chapter, you will learn how to change an equation from standard form to slope-intercept form.

When given the slope (m) and y-intercept (b) all you need to do is plug the numbers into the correct spot in the formula (y = mx+b).

“YouTube.” Youtube-Nocookie.com, 2022, www.youtube-nocookie.com/embed/tMXzBKm3SSA?playlist=tMXzBKm3SSA&amp;autoplay=1&amp;iv_load_policy=3&amp;loop=1&amp;modestbranding=1&amp;start=. Accessed 13 Nov. 2022. “YouTube.” Youtube-Nocookie.com, 2022, www.youtube-nocookie.com/embed/qE463XcV1Ro?playlist=qE463XcV1Ro&amp;autoplay=1&amp;iv_load_policy=3&amp;loop=1&amp;modestbranding=1&amp;start=. Accessed 13 Nov. 2022. “YouTube.” Youtube-Nocookie.com, 2022, www.youtube-nocookie.com/embed/6-ucOmy-bVY?playlist=6-ucOmy-bVY&amp;autoplay=1&amp;iv_load_policy=3&amp;loop=1&amp;modestbranding=1&amp;start=. Accessed 13 Nov. 2022. “YouTube.” Youtube-Nocookie.com, 2022, www.youtube-nocookie.com/embed/KUe8eAhExS0?playlist=KUe8eAhExS0&amp;autoplay=1&amp;iv_load_policy=3&amp;loop=1&amp;modestbranding=1&amp;start=. Accessed 13 Nov. 2022. “YouTube.” Youtube-Nocookie.com, 2022, www.youtube-nocookie.com/embed/HljBn2f22lg?playlist=HljBn2f22lg&amp;autoplay=1&amp;iv_load_policy=3&amp;loop=1&amp;modestbranding=1&amp;start=. Accessed 13 Nov. 2022. “YouTube.” Www.youtube-Nocookie.com, www.youtube-nocookie.com/embed/xWdTE83WZQ4?playlist=xWdTE83WZQ4&amp;autoplay=1&amp;iv_load_policy=3&amp;loop=1&amp;modestbranding=1&amp;start=.. Accessed 28 Nov. 2022.

Which equation is for parallel lines or perpendicular lines

There are two different types of lines, Parallel and Perpendicular. 	In this chapter, you will learn how to recognize if a line is Parallel or Perpendicular based on an equation.

y = 4x + 2 and y = 4x y = 3x + 2 and y = -1/3x +4 y = -1/5x +8 and y = 5x + 3 y = 1/2x + 5 and y = 1/2x + 6

Tip: If an equation for a line is parallel the slope (m) will be the same Example: y = 2x + 4 and y = 2x + 8 These lines would be parallel because the slope (m) in both equations is the same If an equation of a line is perpendicular to the slope (m) of both equations would be the negative reciprocal (opposite) of each other Example: y = 6x + 2 and y = -1/6x + 4 These lines are perpendicular because -1/6 is the negative reciprocal (opposite) of 6

We all hope you learned a lot from this book!

For linear equations, we can use a variety of formulas.&nbsp;&nbsp; These chapters introduce you to the different types of equations you can use for linear equations, and how you can use them in other units.

The slope formula is used to find the slope of a line using two coordinates on a graph.

You must take both y1 and y2 coordinates and divide them by the x1 and x2 coordinates.

<a href="https://www.youtube-nocookie.com/embed/HljBn2f22lg?playlist=HljBn2f22lg&amp;autoplay=1&amp;iv_load_policy=3&amp;loop=1&amp;modestbranding=1&amp;start=">Video to help understand </a>

Step 1: Replace the variables y1 and x1 with the X and Y coordinates. The Formula- y-y1= m( x- x1) Example:(4,8); Slope = 1 #1. Replace variables with x and y values y - 8 = 1(x - 4) Step 2: Use the Distributive Property Example: y - 8 = 1(x - 4) #2. Distribute 1 (The Slope) to x and -4 y - 8 = x - 4 Step 3: Solve for y Example: y - 8 = x - 4 #3. Isolate y (in this case you would add 8 + (-4) and get a positive 4) Answer: y=x+4

Answer Key: Parallel Perpendicular Perpendicular Parallel

(The Formula.... y - y1 = m(x-x1))

#1. (5,6); Slope = 2 y - 6 = 2(x - 5) (Distribute m) y - 6 = 2x - 10 +6 +6 y = 2x - 4 #3. (2,4); Slope = 1 y - 4 = 1(x - 2) (Distribute m) y - 4 = x - 2 +4 +4 y = x + 2 #5. (1,3); Slope = 1/2 y - 3 = 1/2(x - 1) (Distribute m) y - 3 = 1/2x - 1/2 +3 +3 y = 1/2x + 5/2 #7. (3,1); Slope = 4 y - 1 = 4(x -3) (Distribute m) y - 1 = 4x -12 +1 +1 y = 4x - 11 #9. (8,2); Slope = 3 y - 2 = 3(x - 8) (Distribute m) y - 2 = 3x - 24 +2 +2 y = 3x - 22

#2. (3,6); Slope = 5 y - 6 = 5(x - 3) (Distribute m) y - 6 = 5x - 15 +6 +6 y = 5x - 9 #4. (7,2); Slope = 7 y - 2 = 7(x - 7) (Distribute m) y - 2 = 7x - 49 + 2 +2 y = 7x - 47 #6. (8,4); Slope = 1/2 y - 4 = 1/2(x - 8) (Distribute m) y - 4 = 1/2x - 4 +4 +4 y = 1/2x + 8 #8. (6,5); Slope = 1 y - 5 = 1(x - 6) (Distribute m) y - 5 = x - 6 +5 +5 y = x - 1 #10. (4, 0); Slope = 1 y - 0 = 1(x - 4) (Distribute m) y = x - 4

Sometimes you may encounter a point such as (3,-1) and you will need to input these numbers into a formula (y - y1 = m(x - x1)). 	In this chapter, you will learn how to change the formula y-y1=m(x-x1) into slope-intercept form y=mx+b.

y - y1 = m(x-x1) y1 = -4 m= 4 x1=2

Solve: y-(-2)= 4(x-(2) y + 2 = 4(x-2) (Distribute the slope (4) y +2 = 4x -8 Subtract x1 (-8) by y1 (2) y = 4x-10

<a href="bookcreator://page/ypUcX0qgSUeySk8UdCAOXg/left">Chapter 1: Formulas</a> <a href="bookcreator://page/ypUcX0qgSUeySk8UdCAOXg/left">	Examples: (Point-Slope Form)</a> <a href="bookcreator://page/ypUcX0qgSUeySk8UdCAOXg/left">Videos to Help</a> <a href="bookcreator://page/D737sw_XQNu8Cz3qG3X5Uw/left">Chapter 2: Writing linear equations</a> <a href="bookcreator://page/D737sw_XQNu8Cz3qG3X5Uw/left">	Example of a Graph</a> <a href="bookcreator://page/R4g60LGvSXKsPu3pznk-UA/right">Chapter 3: Equations in Standard form</a> <a href="bookcreator://page/R4g60LGvSXKsPu3pznk-UA/right">	Examples</a> 	 <a href="bookcreator://page/oTQs5Bj7Q4SSleyrUwDAJA/left">Chapter 4: A Point and Slope</a> <a href="bookcreator://page/oTQs5Bj7Q4SSleyrUwDAJA/left">	Examples:</a> <a href="bookcreator://page/YReBB91URyuhxZG9qUEIcA/left">Chapter 5: Types of Lines</a> <a href="bookcreator://page/YReBB91URyuhxZG9qUEIcA/left">Examples:</a>

There are many different formulas we can use for Linear Equations. 	In these chapters you will learn the different types of equations you can use for Linear Equations and how they can be used in other Units of Math.

#1. (5,6); Slope = 2 #3. (2,4); Slope = 1 #5. (1,3); Slope = 1/2 #7. (3,1); Slope = 4 #9. (8,2); Slope = 3

#2. (3,6); Slope = 5 #4. (7,2); Slope = 7 #6. (8,4); Slope = 1/2 #8. (6,5); Slope = 1 #10. (4,0); Slope = 1

The point-Slope Formula is used to write an equation of a line passing through a point on a graph.

The slope-Intercept form is used to represent the slope of a line.

<a href="https://www.youtube-nocookie.com/embed/tMXzBKm3SSA?playlist=tMXzBKm3SSA&amp;autoplay=1&amp;iv_load_policy=3&amp;loop=1&amp;modestbranding=1&amp;start=">Slope Intercept Form Rap</a> <a href="https://www.youtube-nocookie.com/embed/qE463XcV1Ro?playlist=qE463XcV1Ro&amp;autoplay=1&amp;iv_load_policy=3&amp;loop=1&amp;modestbranding=1&amp;start=">Review of slope + Slope-intercept Form</a> <a href="https://www.youtube-nocookie.com/embed/6-ucOmy-bVY?playlist=6-ucOmy-bVY&amp;autoplay=1&amp;iv_load_policy=3&amp;loop=1&amp;modestbranding=1&amp;start=">Linear Equations in Point-Slope Form </a>

2x + 3y = 2 5x + 2y = 10 4x + 6y = 24 3x + 8y = 40

Answer Key: y= -2/3x + 2/3 y= -5/2x + 5 y= -2/3x + 4 y= -3/8x + 5

<a href="https://www.youtube-nocookie.com/embed/xWdTE83WZQ4?playlist=xWdTE83WZQ4&amp;autoplay=1&amp;iv_load_policy=3&amp;loop=1&amp;modestbranding=1&amp;start=">Converting an Equation from Standard form to Slope-Intercept form</a>