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

1. Slope-Intercept form: y = mx + b2. Standard Form: Ax + By = C3. Point-Slope form: y – y1 = m (x – x1)

3 Different Forms of a Linear Equation

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

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

A + B C x y =

Standard Form of a Linear Equation

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

3x + 4(0) = 8 3x = 8 x = 8 3

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 = 2

Ordered pair = (8/3, 0)

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.

Step 2. Find the y-intercept.

Step 3. Plot both ordered pair and draw the line.

-5x – 2(0) = 10 -5x = 10 x = -2 (-2, 0)

-5(0) – 2y = 10 -2y = 10 y = -5 (0, -5)

What is the slope of the line?

Write y = x + 6 in standard form using integers.23

Transform a Linear Equation into Standard Form

Ax + By = C

y = x + 623

3y = (3) x + (3)623

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

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 hourMowing lawns $12

Deliveringnewspapers $5

Job

Real-world: Write a Linear Equation in Standard Form

Define variables.

x = number of hours mowingy = number of hours delivering

Write an equation relating variables

12x + 5y = 130