Please close your laptops and turn off and put away your cell phones, and get out your note-taking materials. Today’s daily 5-minute quiz will be given at the end of class.

Note to teachers: You can use item analysis to see which questions your section missed most on last Thursday’s Weekly Quiz 3, and you can insert slides here with screen shots of those questions you want to go over in class. (I added the two word problems from that quiz to the homework assignment due tomorrow, so if you go over them in class, they should be prepared to do them themselves in the homework again.) It may also be helpful if you use the “export data” function on Practice Weekly Quiz 3 (export all attempts) to get an idea of how many times the average student took the practice quiz and how many didn’t take it at all – there seemed to be a lot of those this time around…

Grade Scale Weekly Quiz 3 Results: Average class raw score: __________ Average class score after partial credit: _______ (Letter grade: ___) Practice quiz data: Average number of attempts: _______ Average best score: _______ Maximum number of attempts: _______ Number of students who didn’t take it: _______ (Remember, the weekly practice quiz is a required, 4-point assignment!) Commonly missed questions: #_______________

Quiz question # ____ (xx%)

Please CLOSE YOUR LAPTOPS, and turn off and put away your cell phones, and get out your note- taking materials.

Graphing Linear Equations 2 Sections 3.5/8.1 (HW 15)

Review of formulas covered in Chapter 3:

Note: You can use a printed copy of the sheet containing formulas on quizzes/tests. Yellow handout copies for you to keep are available here and in the open lab. ( You can also view/print a copy of the formula sheet online by clicking on the “Formula sheet” menu button.) Keep a copy of this sheet in your notebook to use while you do your homework assignments and practice quizzes/tests so you know which ones will be available to you on the sheet and where to find them. Clean copies will be handed out for your use at each quiz/test, so you may write notes on your own copy, but you won’t have those notes available as you take the quiz in class.

Find the equation of the line through (-4,0) and (6,-1). Write the equation in standard form. First find the slope. Last session we applied the point-slope formula to problems in which we were given the slope and one point on the line. Example: What if we’re given TWO POINTS on the line? Today we’ll be applying the point-slope formula to problems with different sets of information:

Example (cont.) Now substitute the slope and either one of the points into the point-slope formula. For standard form, clear fractions by multiplying both sides by 10. (use distributive property) (add x to both sides) (This would give but we need standard form.)

Problem from today’s homework: Answer in slope-intercept form: y = -1/3x +10/3 Answer in standard form: x + 3y = 10

Nonvertical parallel lines have identical slopes. Nonvertical perpendicular lines have slopes that are negative reciprocals of each other. Remember: If you rewrite linear equations into slope-intercept form (i.e. solve for y), you can easily determine the slope. Quick review: parallel and perpendicular lines

Find an equation of a line that contains the point (3,-5) and is perpendicular to the line 3x + 2y = 7. Write the equation in slope-intercept form. First, we need to find the slope of the given line. 2y = -3x + 7 (subtract 3x from both sides) Example (divide both sides by 2) Since perpendicular lines have slopes that are negative reciprocals of each other, we use the slope of for our new equation, together with the given point (3,-5).

Example (cont.) (multiply by 3 to clear fractions) (use distributive property) (subtract 15 from both sides) (divide both sides by 3) (simplify)

First, we need to find the slope of the given line. 3y = -x + 6 (subtract x from both sides) Example: y = x + 2 (divide both sides by 3) Since parallel lines have the same slope, we use the slope of for our new equation, together with the given point. Find an equation of a line that contains the point (-2,4) and is parallel to the line x + 3y = 6. Write the equation in standard form.

(multiply by 3 to clear fractions) (use distributive property) (add x to both sides) (Why? Because they want it in STANDARD form) (add 12 to both sides) Example (cont.) What would this look like in slope-intercept form?

Find the equation of the line parallel to y = -4, passing through the point (0,-3). The line y = -4 is a horizontal line (slope = 0). If the new line is parallel to this horizontal line y = -4, then it must also be a horizontal line. So we use the y-coordinate of our point to find that the equation of the line is y = -3. NOTE: Sketching a quick graph of the line y = -4 and the point (0,-3) can help you visualize the situation and make sure you are solving the problem correctly. Example:

Find the equation of the line perpendicular to x = 7, passing through the point (-5,0). The line x = 7 is a vertical line. If the new line is perpendicular to the vertical line x = 7, then it must be a horizontal line. So we use the y-coordinate of our point to find that the equation of the line is y = 0. Again: Sketching a quick graph of the line x = 7 and the point (-5,0) can help you visualize the situation and make sure you are solving the problem correctly. Example

Application problems that involve figuring out the equation of a line:

The assignment on this material (HW 15) is due at the start of the next class session. Lab hours in 203: Mondays through Thursdays 8:00 a.m. to 7:30 p.m. Please remember to sign in!

Please open your laptops, log in to the MyMathLab course web site, and open Daily Quiz 13. You have 5 minutes to finish this quiz. If you finish the quiz problems in less than 5 minutes, remember to check your work and your online answers before submitting the quiz. After you submit your quiz, turn your worksheet in to the TA, and then you are free to leave.