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M118 Weeks 8 &amp; 9

# M118 Weeks 8 &amp; 9 - Your course grades at midterm...

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Unformatted text preview: Your course grades at midterm are viewable in the WEBWORK gradebook. Your grade has been computed using the following weightings: Webwork : 10% (only best 6 out of 9 counted) Test 1 45% Midterm 45% IF YOUR COURSE GRADE AT MIDTERM IS A “D” OR LOWER, YOUR CHANCES OF PASSING THE CLASS (with at least a “C-” ARE NOT VERY HIGH!!!! LAST DAY FOR AUTOMATIC “W” IN CLASS!!- After this date, you must petition your Dean (with a VERY good reason) to be able to withdraw from the course.- Incompletes are NOT an option (Incompletes are only given to students who have completed the entire course with a passing grade but who are unable to take the final exam due to illness, etc.) PART 2: LINEAR MODELS DEFN: A linear equation linear equation is any equation of the form Ax + By = C, where A, B, and C are real numbers and A and B are not both zero. DEFN: The graph of the set of all points (x,y) that make a linear equation true is called a line. line. Parts of the line Ax + By = C 1.) slope = -A/B 2.) x-intercept = C/A 3.) y-intercept = C/B slope-intercept form: slope-intercept form: y = mx + b, where m = slope, b = y-intercept C/B C/A 2 SPECIAL CASES: 1.) By = C slope = 0 x-intercept = none y-intercept = C/B 2.) Ax = C slope = undefined x-intercept = C/A y-intercept = none C/B By=C Ax=C C/A Rules for working with lines: Rule 1: Given any two points on a line, (x 1 , y 1 ) and (x 2 , y 2 ), the slope of the line is given by m = (y 2- y 1 ) / (x 2- x 1 ). Rule 2: If two lines are parallel, then they have the same slope. Rule 3: To graph a line, find two points on it, plot them and connect. Rule 4: To find the equation of a line given it’s slope m slope m and a point (x point (x 1 , y , y 1 ) a.) plug the slope m into y = mx + b. b.) plug the point (x 1 , y 1 ) into the resulting equation. c.) solve the equation for b. d.) rewrite the equation using the value of b found in part c.). 1.) Find the equation of the line with slope m = 4 and x-intercept 3. 2.) Find the equation of the line that passes through the points (1,4) and (-2, -3). 3.) Find the equation of the line that passes through the point (5,2) and is parallel to the line 3x + 5y = 8. Example: A linear relationship exists between the number of years you study math and the amount of money you will need to spend on therapy to get over it. If you study math for 2 years, you will need to spend \$800 on therapy, and if you spend 10 years studying math, you will need to spend \$9600 to get over it. a.) Find a linear equation that expresses the above relationship b.) Graph the line found in part a.) c.) If you study math for 20 years, how much will you need to spend on therapy to get over it? d.) If you end up spending \$53,600 on therapy, for how long did you study math? Given: 2 lines Ax + By = C Dx + Ey = F What can we say about the point (s, t) ?...
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