1. 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 1. Slope-Intercept form: y = mx + b 2. Standard Form: Ax + By = C 3. Point-Slope form: y – y 1 = m (x – x 1 ) 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

2. 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)

3. 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)

4. 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?

5. Write y = x + 6 in standard form using integers. 2323 Transform a Linear Equation into Standard Form Ax + By = C y = x + 6 2323 3y = (3) x + (3)6 2323 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

6. 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 Mowing lawns $12 Delivering newspapers $5 Job Real-world: Write a Linear Equation in Standard Form Define variables. x = number of hours mowing y = number of hours delivering Write an equation relating variables 12x + 5y = 130