Section 6-3: Standard Form of a Linear Equation SPI 22C: select the graph that represents a given linear function

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Section 6-3 Standard Form of a Linear
EquationSPI 22C select the graph that
represents a given linear function
Objective Graph and write linear equations in
standard form
Vocabulary

• x- Intercept
• point where line crosses the x-axis

• y- Intercept
• point where line crosses the y-axis

3 Different Forms of a Linear Equation
1. Slope-Intercept form y mx b 2.
Standard Form Ax By C 3. Point-Slope form
y y1 m (x x1)
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Standard Form of a Linear Equation
A B C
x y
A, B, and C are real numbers,
and A and B are not both zero.
The x and y are an ordered pair.

• Use the x-intercept and y-intercept to graph.
• x-intercept is where line crosses x-axis (x,0)
• y-intercept is where line crosses y-axis (0,y)

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Caution The slope is not the value in front of
the x term in the standard form.
Graph Standard Form of a Linear Equation
Graph the equation 3x 4y 8.

• Step 1. Find the x-intercept.
• Substitute 0 for y in the equation
• Solve for x and write the ordered pair

3x 4(0) 8 3x 8 x 8
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Ordered pair (8/3, 0)

• Step 2. Find the y-intercept.
• Substitute 0 for x in the equation
• Solve for y and write the ordered pair

3(0) 4y 8 4y 8 y
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Ordered pair (0, 2)
Step 3. Plot both ordered pair and draw the line.
(8/3, 0) (0, 2)
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Do Now
Graph Standard Form of a Linear Equation
Graph the equation -5x 2y 10.
Step 1. Find the x-intercept.
What is the slope of the line?
-5x 2(0) 10 -5x 10
x -2 (-2, 0)
Step 2. Find the y-intercept.
-5(0) 2y 10 -2y 10
y -5 (0, -5)

Step 3. Plot both ordered pair and draw the line.
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Transform a Linear Equation into Standard
Form
2 3
Write y x 6 in standard form using
integers.
Ax By C
2 3
y x 6
2 3
3y (3) x (3)6
Multiply each term by 3 to form integers
3y 2x 18
Simplify
-2x 3y 2x 18 2x
Subtract 2x from both sides (SPE)
-2x 3y 18
Simplify
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Real-world Write a Linear Equation in
Standard Form
Write an equation in standard form to find the
number of hours you would need to work at each
job to make a total of 130.
Amount Paid per hour
Job
Mowing lawns
12
Delivering newspapers
5
Define variables.
x number of hours mowing y number of hours
delivering
Write an equation relating variables
12x 5y 130