Transcript 6-3 PPT Standard Form

Section 6-3: Standard Form of a Linear Equation
SPI 22C: select the graph that represents a given linear function
Objective:
Graph and write linear equations in standard form
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)
Standard Form of a Linear Equation
Ax + B y = C
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)
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
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
3x + 4(0) = 8
3x = 8
x=8
3
3(0) + 4y = 8
4y = 8
y=2
Ordered pair = (0, 2)
Step 3. Plot both ordered pair and draw the line.
(8/3, 0)
(0, 2)
Graph Standard Form of a Linear Equation
Graph the equation -5x – 2y = 10.
Step 1. Find the x-intercept.
-5x – 2(0) = 10
-5x = 10
x = -2
(-2, 0)
What is the
Step
2. Find
y-intercept.
slope
ofthethe
line?
-5(0) – 2y = 10
-2y = 10
y = -5
(0, -5)
Step 3. Plot both ordered pair and draw the line.
Transform a Linear Equation into Standard Form
Write y = 2 x + 6 in standard form using integers.
3
Ax + By = C
y = 2x + 6
3
3y = (3) 2 x + (3)6
3
3y = 2x + 18
Multiply each term by 3 to form integers
Simplify
-2x + 3y = 2x + 18 – 2x
Subtract 2x from both sides (SPE)
-2x + 3y = 18
Simplify
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.
Job
Mowing
lawns
Delivering
newspapers
Amount Paid
per hour
$12
$5
Define variables.
x = number of hours mowing
y = number of hours delivering
Write an equation relating variables
12x + 5y = 130