Slope, XY-Intercepts, Graphing Linear Functions in Standard Form

Graphing Linear Functions in Standard Form

by Dr. Cynthia O. Williams

Linear Equations

Standard form, slope-intercept form, and point-slope form.

Multiple Choice

What is the formula for standard form?

• $$y=mx+b$$

• $$y-y_1=m\left(x-x_1\right)$$

• $$Ax+By=C$$

• $$\frac{rise}{run}$$

The slope of a line...

• is how steep the line is between two points.

• can be positive, negative, 0, or undefined.

• determines if the line rises, falls, is horizontal or vertical.

Slope from a Graph

​You can also use DESMOS

Identifying Slope of a Line

• Slope can tell us the direction of the line!

• Refresh yourself of the 4 types of slope using the picture to the right:

Slope from 2 Points

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

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 STANDARD FORM of a line is written as. . .

​Ax + By = C

​​Such as 3x + 2y = 12, 4x - y = 8, or ​-5x + 8y = 10

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​You bought 2 burgers and 3 fries, and paid a total of $18. The equation in STANDARD FORM is ​

2b + 3f = 18

​We can graph the function of this equation

2x + 3y = 18

Remember x = burgers and y = fries

The easiest what to graph a line written in Standard Form is to find the x-intercept and the y-intercept of the equation and graph those two points.

Let's take a look

Click to watch this video

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Click 'Next" when done.

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​Now that you have seen how to graph from STANDARD FORM, let's graph the burger and fries problem.

2x + 3y = 18

x-int: (9, 0)

y-int: (0, 6)

Linear Equations

Standard form, slope-intercept form, and point-slope form.

Multiple Choice

What is the standard form equation?

• y=mx+b
• Ax+By=C
• y-y₁=m(x-x₁)
• y=b-x

Multiple Choice

Which equation is written in STANDARD form?

• y = 1/2x + 2

• y - 3 = -5(x + 2)

• 7x - 2y = -9

• 3x + 2 = y

Multiple Choice

What is the y-intercept of 2x - 5y = 20

• (10, 0)

• (-4, 0)

• (0, 10)

• (0, -4)

Multiple Choice

What is the x-intercept of 2x - 5y = 20

• (10, 0)

• (-4, 0)

• (0, 10)

• (0, -4)

Multiple Choice

What are the x and y intercepts to use when graphing 3x + 4y = -12?

• (0, 4) and (3, 0)

• (0, -4) and (-3, 0)

• (0, -4) and (3, 0)

• (0, 4) and (-3, 0)

Multiple Choice

Given the graph below, what are the x and y intercepts? 

• x = -2 and y = 1
• x = 1 and y = -2

Multiple Choice

Name the x- and y-intercepts for the equation:
5x - 3y = 15

• (3, 0) and (0, -5)
• (0, 3) and (-5, 0)
• (5, 15) and (15, 3)
• (0, -3) and (5, 0)

Multiple Choice

Which graph represents 2x + 4y = 12?

Multiple Choice

What is the y-intercept?

• 2
• 3
• 4
• -2

Multiple Choice

What are the x- and y-intercepts of the linear function given by the equation x + y = -2

• (-2, -2)

• (-2, 0) and (0, -2)

• (0, 0)

• (2, 0) and (0, 2)

Multiple Choice

What is the x intercept of the graph?

• 4

• 1

• -4

• cannot be determined

Multiple Choice

What is the y-intercept of
2x-5y=35?

• (0,-7)
• (-7,0)
• (35/2, 0)
• (0,35/2)

Multiple Choice

Name the x- and y-intercepts for the equation:
2x - y = 6

• (0, 3) and (-6, 0)
• (0, -3) and (-6, 0)
• (3, 0) and (0, -6)
• (-3, 0) and (0, -6)

Multiple Choice

What is the y- intercept of the graph of 3x+4y=24

• 5
• -5
• 6
• -6

Multiple Choice

Graph 6x - 5y = -15

Multiple Choice

What are the x- intercepts of the graph of 3x+4y=24

• 8
• -8
• 6
• -6

Multiple Choice

Graph 3x - y = 5