Linear Equations

Jaime Bennett

Algebra

1/28/08

Aim: How do we write the equation of a line in standard form? Warm up: 1. Write in standard form and determine the slope and y-intercept: a. 2x + 4y = -8 b. -5x – y = 12 2. Determine if the point lies on the line: a. (1,-3); 2x + 4y = -8 b. (3,-3); -5x – y = 12 Lesson: • •

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What is the standard equation of a line? (y = mx + b) o What does m represent? o What does b represent? What is the equation of a line with slope 3 and y-intercept 7? o What is the standard formula for a line? o 3 represents which variable? o 7 represents which variable? o Set up the equation; y = 3x + 7. Find the equation of a line with slope -4 y-intercept -2 . o Is this graph increasing or decreasing? o How do we determine this? Find the equation of a line with slope ½ and y-intercept (0,3) o Is it possible to have a fraction as a slope? o How would you interpret this slope if you were graphing the line? o Which coordinate of the point is ‘b’? o Why is the x-value 0 for the y-intercept? Determine the equation of a line with slope 5 and passing through the point (0,-1) o How can we write the equation when we don’t know ‘b’? o Is this graph increasing or decreasing? Students will work on the next 6 examples. They will put their work on the board and we will discuss the solutions: Write the equation of the line satisfying the given conditions: 1. slope= (-5/3); y-intercept 4 2. m= 2; y-intercept -4 3. Slope: -7 and y-intercept (0,-3) 4. Slope: 4 and passing through (0,1) 5. Slope: ½ and passing through the origin 6. Parallel to the line y=2x + 12 and passing through (0,3)

Closure: 1. What two variables must you know in order to write the equation of a line? 2. Do you think it is possible to write the equation of a line if we aren’t given the yintercept?

Homework: See attached sheet! Jaime Bennett

Algebra

1/29/08

Aim: How do we write the equation of a line given the slope and a point on the line? Warm up: 1. John is building a rectangular garden. The length of the garden is 3 feet more than the width. If the area of the garden is 54 feet², find the dimensions of the garden. 2. Determine the slope and y-intercept of the equation: -x + 4y = -16 3. Write the equation of a line with slope -1 and passing through (0,5) Lesson: We will start the lesson by recalling yesterday’s lesson. We will discuss the warm-up and why that point is easy. Then the next example; students will be given the slope and a random point on the line. Students will get the chance to discuss their ideas as to how to approach the problem. We will work on 4 examples together substituting points to find b in order to write the equation. Then we will write the equation of a line reading it off of a graph. Students will have to be able to identify the y-intercept and the slope by moving along the line. To end the class students will create three examples based on the examples from today and yesterday. They will switch papers with their partner who will try and write the equation of the line given the information. I will collect the papers before they leave. Their partner is responsible for ‘grading’ the work. Closure: 1. What does it mean if the point has 0 for its x value? Homework: See attached sheet! Jaime Bennett

Algebra

1/29/08

Aim: How do we write the equation of a line given the slope and a point on the line? Warm up: 1. Write the equation given the following information: a. m = 4, y-intercept 5 b. Slope 1/3 (0,-2) c. m = -3, passing through (0,0) 2. Find the slope between the give points: a. (5,4) and (3,-6) b. (6,1) and (6,-8) Lesson: Students will spend the period practicing writing equation given a slope and the yintercept or just a point on the line. This will help to reinforce the idea before we move into the next topic. If there is time remaining we will take some examples from the end of yesterdays lessons and put them on the board for us to try as a class. Closure: 1. How would we write the equation of a line given two points?

Homework: See attached sheet! Jaime Bennett

Algebra

1/30/08

Aim: How do we write the equation of a line given two points? Warm up: 1. Find the slope between the given points: a. (3,4) and (5,8) b. (-2,3) and (2, 5) Lesson: •

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Example 1: Write the equation of a line passing through the points (3,4) and (5,8). o How do we write the equation of a line? o First we need to find ‘m’, any thoughts? o Which point should we use to find ‘b’? Does it matter? Example 2: Write the equation of a line passing through the points (-2,3) and (2, 5). o Why isn’t the slope undefined? o Does it matter which point you use to solve for b? Example 3: Write the equation of a line passing through the points (4,1) and (-7,1). o How do we find slope? o Why is our slope 0? o How would you explain what this line looked liked if we were to graph it? o Why isn’t there an x in our formula? Example 4: Determine the equation of the line passing through (5,4) and (5,-7). o Why can’t we divide by zero? o How does this affect the graph? o Do you notice anything interesting about our two given points? o Why isn’t this equation written as y equals? Students will try example 5 and 6 on their own: o Example 5: Determine the equation of the line passing through (2,3) and (6,-9). o Example 6: Determine the equation of the line passing through (1,7) and (-6,0). (BE CAREFUL!)

Closure: 1. Why do you need to find the slope when given two points in order to write the equation of a line? 2. What does it mean if the slope is undefined? How does the equation of the line change? Homework: See attached sheet!

Jaime Bennett

Algebra

1/31/08

Aim: How do we write the equation of a line given two points? Warm up: 1. Find the equation of the line passing through (-7,1) and (5,9) Lesson: Students will be given a note card with a point on the note card. They will have to pair up with 10 different people to create 10 different equations. Every student has a different point so it won’t be as difficult to find 10 different lines. No one will have a yintercept in order to keep it challenging. They will be allowed to look in their notes to recall the procedure to writ the equation. This will be a strong wrap up before their quiz next period. We will collect the 10 examples at the end of class to be graded. Closure: 1. How do we read a graph in order to write the equation? 2. What does it mean if the slope is 0? How does the equation of the line change? Homework: See attached sheet! Jaime Bennett

Algebra

1/31/08

Aim: Quiz Warm up: 1. Write the equation on a line passing through (2,5) and with a slope of ½ 2. Find the slope between (-2,4) and (1, -5) 3. Write in standard form: 3x + 2y = -8 4. Does (-1,-1) lie on x + y = -2 Lesson: Students will have most of the period to work on their quiz. When they finish they will continue working on their lines packet. Homework: See attached sheet!

Name:_______________________________

Algebra

1. Write the equation of a line whose Slope = 2, and y-intercept -6

2. Write the equation of a line parallel to 3y = 6x – 9 and passing through (0,-4)

3. Determine the equation of the given graph:

4. Write the equation of the line passing through

5. Write the equation of the line passing through (-2,1) and (-2,3)

6. Write the equation of the line

7. Determine the equation of a line which passes through the origin and (4,-8) Jaime Bennett

Algebra

1/31/08

Aim: How do we Solve systems of linear equations? Warm up: Write the equations in standard form: a. 3x – 4y = 12 b. 5 – y = 19

c. -5y = 15

Lesson: Students will work in groups of two graphing lines. Each student will be given a different colored pencil. They will have four graphs in front of them. One student will graph one of the lines and then they will switch papers. Then that student will graph their line on the same graph. Once they have the two lines on their paper we will discuss if anyone knows what the solution may be. They will complete the second problem the same way with switching. Then they will graph the last two examples on their own determining the solution. Closure: 1. Why is a point the solution to the system of equations? Homework: See attached sheet!