Standard Form and Intercepts

Standard Form and Intercepts

By Roman

Standard Form is one of three key ways we write linear functions.

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In the visual to the right, we have the general equation of Standard Form. A, B, and C represent integers, while x and y are variables.

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Standard Form

Intercepts are where a linear function crosses the x or y-axis.

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We call them the x-intercept and the y-intercept.​

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Intercepts

The x-intercept is an ordered pair that follows this form: (x , 0)

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​This means the point doesn't go up or down. Only left or right.

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It is where the function crosses the x-axis. Hence "x-intercept"

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x-intercepts are also called "solutions" because they help us sketch graphs with unknown behavior

The x-intercept

The y-intercept is an ordered pair that follows this form: (0, y)

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​This means the point doesn't go left or right. Only up or down.

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It is where the function crosses the y-axis. Hence "y-intercept"​

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y-intercepts have many real world applications such as starting point or starting money.

The y-intercept

Standard Form and Intercepts

We find intercepts easily using the Standard Form

Since we know ordered pairs represent solutions to a linear equation, we can use the fact that the intercepts are (x , 0) and (0 , y) to solve for either x or y.

Really recall how we solved equations back in October.

Open Ended

Lets say we have a linear equation in Standard Form: $$3x+4y\ =12$$  

When you plug in 0 for x, what is our new equation?

Open Ended

Lets say we have the same linear equation in Standard Form: $$3x+4y\ =12$$

When we plug in 0 for y, what is our new equation?

Plug 'n' Chug Pt. 1

Because for each intercept we know that the other variable is equal to 0, we can easily solve for either x or y by plugging in 0.

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Plug 'n' Chug is necessary for solving many equations, and will be a necessary skill when evaluating functions.

Plug 'n' Chug Pt. 2

For example: 3x + 4y = 12; We know the x-intercept will be (​x, 0)

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​We replace y with 0: 3x + 4(0) = 12

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We can solve for x how we normally do, and we arrive at: x = 4

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The x-intercept as such should be (4,0).

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Fill in the Blanks

Solve for the y-intercept of the linear equation: $3x+4y\ =12$

State your answer in the form of an ordered pair.

Wrap-Up

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We can use Standard Form to find the x and y-intercepts of a linear equation. Soon, we can start to use it to find the slope, but for now we'll leave it here.

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Please complete the last few questions and Press "submit" on Google Classroom.

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Subject | Subject

Some text here about the topic of discussion

Multiple Choice

Find the x and y intercepts for the following linear equation in Standard Form:

$$5x+3y=15$$  

• x: (5,0)

  y: (0,3)

• x: (0,5)

  y: (0,3)

• x: (-5,0)

  y: (0,-3)

• x: (-5,0)

  y: (3,0)

Multiple Choice

Find the x and y intercepts for the following linear equation in Standard Form:

$$6x-4y=24$$  

• x: (24,0)

  y: (6,-4)

• x: (-4,0)

  y: (0,6)

• x: (0,4)

  y: (0,-6)

• x: (4,0)

  y: (0,-6)

Multiple Choice

Find the x and y intercepts for the following linear equation in Standard Form:

$$2x-9y=-18$$  

• x: (9,0)

  y: (0,-2)

• x: (-9,0)

  y: (0,2)

• x: (2,-9)

  y: (-18,0)

• x: (0,-9)

  y: (2,0)

Fill in the Blanks

Write the general equation for Standard Form.