MTH4151-relationship between two linear functions

Relationship between two linear functions

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Quiz

Math

4. Slopes are not the same & product of the slopes does not equal -1 -> intersecting

3. Slopes are not the same & producte of the slope equals -1 -> perpendicular

2. Slopes are the same Y-intercepts are the same -> parallel & coincident

1. Slopes are the same y-Intercepts are different -> parallel & distinct

Compare the slope and y-intercept values of two linear function to determine their relationship.

Review

1. "y" is already isolated in the equation.Extract slope (value with x) and y-intercept (value without x)

There are 3 ways you can determine the slope and y-intercept values of a linear funciton.

Review

2. Need to transform the equation to isolate the 'y' variable.Then extract the slope & y-intercept value.

There are 3 ways you can determine the slope and y-intercept values of a linear funciton.

Review

3. Calculate the slope and y-intercept values.

There are 3 ways you can determine the slope and y-intercept values of a linear funciton.

Review

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Once you have determined the slopes & y-intercept... Step 1: Compare the slope values. 2a. If the slopes are the same, compare the y-intercept values. If slopes are the same but the y-intercepts are different -> parallel & distinct If slopes are the same and the y-intercepts are the same -> parallel & coincident 2b. If the slopes are not the same, multiply the two slopes. (not necessary to compare the y-intercepts in this case) If multiplying the two slopes equals to -1 -> perpendicular If multiplying the two slopes does not equal to -1 -> intersecting *Write down some notes before continuing to the exercises.

Review

1/5

Follow the step-by-step prompts to determine the relationship between the these two linear functions. Click on the picture to enlarge it.

1/5

Follow the step-by-step prompts to determine he relationship between the these two linear functions. Click on the picture to enlarge it.

1/5

Follow the step-by-step prompts to determine the relationship between the these two linear functions. Click on the picture to enlarge it.

1/5

Follow the step-by-step prompts to determine the relationship between the these two linear functions. Click on the picture to enlarge it.

1/5

Follow the step-by-step prompts to determine the relationship between the these two linear functions. Click on the picture to enlarge it.

1/5

Follow the step-by-step prompts to determine the relationship between the these two linear functions. Click on the picture to enlarge it.

1/5

Follow the step-by-step prompts to determine the relationship between the these two linear functions. Click on the picture to enlarge it.

1/5

Summary

2/5

Follow the step-by-step prompts to determine the relationship between the these two linear functions. Click on the picture to enlarge it.

2/5

Follow the step-by-step prompts to determine the relationship between the these two linear functions. Click on the picture to enlarge it.

Don't remember? Click on the lightbulb for hints!

2/5

Follow the step-by-step prompts to determine the relationship between the these two linear functions. Click on the picture to enlarge it.

Don't remember? Click on the lightbulb for hints!

2/5

Isolate 'y' in the 5y - 2x = 1 eqution. *Hints: minus becomes plus multiplication becomes division

2/5

Now that the 5y - 2x = 1 is transformed into y = 0.2 + 0.4x

2/5

Now that the 5y - 2x = 1 is transformed into y = 0.2 + 0.4x

Don't remember? Click on the lightbulb for hints!

2/5

Now that you have both slopes and y-intercepts from both equations... What's next?

2/5

Now that you have both slopes and y-intercepts from both equations... Wha's next?

Don't remember? Click on the lightbulb for hints!

2/5

Now that we have established that the slopes are the same, what's next?

2/5

Now that we have established that the slopes are the same, what's next?

2/5

summary

3/5

Follow the step-by-step prompts to determine the relationship between the these two linear functions. Click on the picture to enlarge it.

3/5

Follow the step-by-step prompts to determine the relationship between the these two linear functions. Click on the picture to enlarge it.

slope = -0.5

slope = 4

slope = 3.5

slope = 2.5

Don't remember? Click on the lightbulb for hints!

3/5

Calculate the slope of the straight line that passes through (0,2) and (-4, -12)

y-intercept = 2

y-intercept = 0

y-intercept = -26

Don't remember? Click on the lightbulb for hints!

3/5

Calculate the y-intercept of the straight line that passes through (0,2) and (-4, -12)

Don't remember? Click on the lightbulb for hints!

Now that you have both slopes and y-intercepts from both functions... What's next?

3/5

Don't remember? Click on the lightbulb for hints!

Now that you have both slopes and y-intercepts from both functions... What's next?

3/5

Now that we have established that the slopes are the same, what's next?

Don't remember? Click on the lightbulb for hints!

3/5

Now that we have established that the slopes are the same, what's next?

Don't remember? Click on the lightbulb for hints!

3/5

Don't remember? Click on the lightbulb for hints!

3/5

summary

Don't remember? Click on the lightbulb for hints!

y = 4x + 5

y = -4x + 2.5

y = -8x + 3

Follow the step-by-step prompts to determine the relationship between the these two linear functions. Click on the picture to enlarge it. 1. Isolate the 'y' variable in 2y + 8x -5 =0

4/5

Now that 2y + 8x -5 = 0 is transformed into y = -4x + 2.5

4/5

Now that 2y + 8x -5 = 0 is transformed into y = -4x + 2.5

4/5

Don't remember? Click on the lightbulb for hints!

y = 0.8x +0.8

y = 1.25x -9

y = 0.25x -5

Determine the equation of the straight line that passes through (4, -4) and (-4, -6)

4/5

Now that we have determine the straight line that passes through (4,-4) and (-4, -6) can be represented as y = 0.25x - 5

4/5

Now that we have determine the straight line that passes through (4,-4) and (-4, -6) can be represented as y = 0.25x - 5

4/5

Don't remember? Click on the lightbulb for hints!

Parallel & distinct Slope are the same. Y-intercept are different.

Perpendicular Slopes are different. Multiply the two slope equal to -1

Intersecting Slopes are different. Multiply the two slopes does not equal to -1

Determine the relationship between these two linear functions.

4/5

Summary

Parallel & distinct Slope are the same. Y-intercept are different.

Intersecting Slopes are different. Multiply the two slope equal to -1

Perpendicular Slopes are different.Multiply the two slope equal to -1

5/5

Determine the relationship between these two linear functions. Click on the picture to enlarge it.

Summary

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