6.2 Equation of a Line in Standard Form Analyzing Linear Relations Learning Goals: In this lesson students will learn how to convert an equation in standard form into slope y-­‐intercept form. Students will then be able to determine slope and y-­‐intercept from the equation and relate that to fixed and variable costs in partial variation. DO IT NOW! 1. Is the relation 2x – 3y – 6 = 0 linear? Explain. 2. Determine the y-­‐intercept of this relation by letting x = 0. (Every point on the y-­‐axis has an x-­‐coordinate of zero) 3. Find the coordinates of two other points that are on the graph. Hint: If a point is on the graph, then its coordinates must satisfy the equation (make the equation true). Math 9 – Jensen 6.2 – Standard Form 4. Graph the relation 5. The graph of the relation should be a line. If your graph does not represent a linear relation, check the calculations for the coordinates of the points you used. 6. Use two of the points you found and calculate the slope of the line. 7. Use the slope and the y-­‐intercept to write the equation in slope y-­‐intercept form. 8. Compare the equation you wrote in step 7 to the original equation in step 1. What can you tell about how these equations are related? Math 9 – Jensen 6.2 – Standard Form Standard form of a line is Ax + By + c = 0 where A, B, and C are _____________________ and A and B are both not ________________. Example 1: Write the equation of the line 2x – 3y – 6 = 0 in slope y-­‐intercept form by isolating the y. Example 2: Write each equation in slope y-­‐intercept form and state the slope and the y-­‐
intercept. a) 3x + 5y – 15 = 0 b) 7x – 3y + 21 = 0 Math 9 – Jensen 6.2 – Standard Form Example 3: Barney’s Banquet Facility charges according to the equation 2x – y +200 = 0 where x is the number of people attending and y is the total cost. a) Write the equation in slope y-­‐intercept form. b) What is the fixed cost? c) What is the rate of change of the cost? d) What is the total cost if 125 people attend a banquet at Barney’s? e) If the total cost is $920, how many people attend the banquet? Math 9 – Jensen 6.2 – Standard Form Consolidate: 1. There are two forms in which the equation of a line can be written. What are they? 2. It is possible to convert an equation from one form to the other by ________________________ the Kuta Software - Infinite Algebra 1
Name________________________________
equation. Writing Linear Equations
Date________________ Period_
3. Write the slope-intercept form of the equation of each line.
1) 3 x − 2 y = −16
2) 13 x − 11 y = −12
3) 9 x − 7 y = −7
4) x − 3 y = 6
5) 6 x + 5 y = −15
6) 4 x − y = 1
7) 11 x − 4 y = 32
8) 11 x − 8 y = −48
Write the standard form of the equation of the line through the given point with the given slope.
Homework: pg 312 #1-­‐7,10 BONUS #11 9) through: (1, 2), slope = 7
Math 9 – Jensen 10) through: (3, −1), slope = −1
6.2 – Standard Form