The Weekend!!! • Today is Friday January 11, 2008. • Last Day to turn in your Student Information Sheet!!! • Please sharpen your pencil, pick up your calculator, (3rd & 5th) take out your practice problems and your word problem worksheet. • We will begin with a bell-ringer as soon as the bell rings. Mod 3 Bell-ringer 1. Describe how to write an equation given a slope and one point? 2. What is the y-coordinate for the x-intercept? Summary • Given the slope & y-intercept. 1. Find the slope. 2. Find the y-intercept. 3. What variables represent each? 4. Substitute values (m, b) into equation y = mx+b. Summary • Given the slope and a point: 1. Find the slope. 2. Substitute x, y from given point into equation y = mx + b. 3. Solve to locate y – intercept. 4. Substitute values (m, b) into equation y = mx + b. • David Margolez has been working for Pioneer Engineering since 1990. Each year he gets a $2,100 raise. In 1998, he earned $33,600. – What information do we know? • M= 2,100 • B= • X= 8 • Y= 33,600 – Substitute information into y = mx + b • Between 2000 and 2006, the monthly rent for a one-bedroom apartment increased by $35 per year. In 2004 the rent was $420 per month. • You work at a travel agency and you are given a $1,500 raise at the end of each year. After working 3 years your salary is $21,000. We know how to write an equation when given a slope and y-intercept. We know how to write an equation when given a slope and a point. What do we do when we aren’t given a slope? What if we’re given two points? We still have to find a slope? What do you suggest? Writing an Equation when given two points. (1, 6) (3, 7) • Find slope using slope • What two pieces of formula. information do I need? 6–7 – M? ½ 1–3 – B? 5½ • My slope is ½ • Now choose one of the • 6 = ½ (1) + b given points. 6=½+b • Using the x and y from 5½=b chosen point replace into • Y=½x+5½ equation y = mx + b • Write the equation for y = mx + b Summary • Given two points: y 2 y1 1. Use the formula m to find slope. x 2 x1 2. Chose either of the given points. 3. Substitute x, y from chosen point into equation y = mx + b. 4. Solve to locate y – intercept. 5. Substitute values (m, b) into equation y = mx + b. • Complete problems 8-10 on Practice Worksheet Write the equation of the line below. a) Find the slope of the line. • M = -3/5 b) Find the y- intercept. • Take one of the points on the line, either (-2, 5) or (3, 2) and substitute into y = mx + b. • B = 19/5 c) Y = -3/5 x + 19/5 Summary • Given a graph: 1. Identify 2 points on the line. 2. Use the formula m 2 y y1 to find slope. x 2 x1 3. Chose either of the given points 4. Substitute x, y from chosen point into equation y = mx + b. 5. Solve to locate y – intercept. 6. Substitute values (m, b) into equation y = mx + b. What type of lines are these? Parallel Lines a) Find the slope of the purple line. b) Find the slope of the red line. c) What do you notice? d) Do the lines have the same y- intercept? Conclusion: Parallel lines have the same slope, but different y- intercepts. • Write the equation of a line parallel to the line y = x + 4 that passes through the point (-2, 0). – What is the slope of the original line? – What is the slope of the new line? – Is the new line going to have the same y- intercept? – Find the y-intercept of the new line using the slope and the given point. • Write the equation of a line parallel to the line y = -3x + 1 and passes through the point (4, 2).