4.1 Write Linear Equations by Using a Tables of Values

Transcription

1 4.1 Write Linear Equations by Using a Tables of Values Review: Write y = mx + b by finding the slope and y-intercept m = b = y = x + Every time x changes units, y changes units m = b = y = x + Every time x changes units, y changes units m = b = y = x + Every time x changes units, y changes units m = b = y = x + Every time x changes units, y changes units

2 Finding y = mx + b from a table of values We will still require the slope ( ) and y-intercept ( ) Finding slope from a table: m = difference in y-values difference in x-values Finding the y-intercept from a table: REMEMBER! the y-intercept is a point where the line crosses the y-axis, and the co-ordinates of the y-intercept are (0, y) count backwards using the pattern of the table until you reach x = 0 Example 1 : Find y = mx + b from the table Finding Slope m = difference in y-values difference in x-values m = Finding y-intercept b = y = x + Graph

3 Finding y = mx + b from a table of values continued Example 2 : Find y = mx + b from the table Finding Slope m = m = difference in y-values difference in x-values Finding y-intercept b = y = x + Graph

4 Finding y = mx + b from a table of values - Word Problem At Super Suds Car Wash 4 min of service cost $2.00, 7 min cost $3.50, and 10 min cost $5.00. Write an equation that represents this relationship. Define your variables. minutes (x) cost (y) Slope : 4 7 y - intercept : 10 equation : Graph : What is the cost per minute?

5 4.2 Write Linear Equations by Translating Written Descriptions Make a list of all the words you can use to represent each of the four operations: addition subtraction multiplication division Translate each phrase into a mathematical statement: The sister s age is double the brother s age. Her age equals his age increased by 5 years. His age is 10 more than twice his sister s age. College graduates earn, on average $400, more per month than high school graduates. Her bank investment grew by $100. Canadians use one tenth of their budget to pay for food. $200 in property taxes is deducted from his salary every month. The new route cut her travel time in half. His salary is $100 per week plus 25% of the profits. A clothing sales person makes a straight commission of 60% of sales.

6 Translate each phrase into an equation of the form y = mx + b. (a) His original mark of 30% has increased by 2% each month. months passed (b) A sales manager is paid $4000 per month less $100 for every customer complaint. # of complaints (c) amount paid ($) A rare coin was purchased for $10. The coin is increasing in value by $2 every month. months passed (b) mark (%) value ($) What will the card be worth four years from its purchase? ( Hint : convert four years to months by multiplying by 12)

7 4.3 Rearrange Equations from One Form to Another Review: The Two Forms of a Linear Equation Slope and Y - Intercept Form Standard Form y = mx + b Ax + By + C = 0 m & b are integers A, B, & C are integers y = mx + b -----> Ax + By + C = 0 Steps: Move all terms to left Put in order Ax + By + C = 0 Remove fractions multiply by denominator Remove decimals multiply by 10 If A is negative, multiply everything by -1. a) y = - 3x - 2 b) y = 2x + 1 c) y = 2x d) y = 2 3 x e) y = 0.2x

8 Partial Ax + By + C = 0 a) 12y + 3x 8 =0 b) 2x 7 3y = 0 c) 2 5 x + 6 y = 0 d) 3x + 6.2y 4 = 0 e) x + 2y 4 = 0 Ax + By + C = > y = mx + b Steps: Move everything except y-term to right a) 3x + y +2 = 0 Divide all terms by coefficient of y Make sure the order is y = mx + b b) -2x + y = 10 c) 4x 5y 20 = 0 d) 3x - 4y + 12 = 10 e) -2x + 4y + 12 = 0 f) 2x + 3y + 1 = 0

9 4.4 Special Cases Back to Basics Graph the line y = 0.5x - 2 without using any shortcuts. A graph is made from points Each point has two coordinates We find points with a table of values To make a table of values, we randomly pick one of the coordinates The equation tells us how to find the other coordinate Any point on the graph satisfies the equation Graph y = 2 Remember, one point is picked randomly, the other is determined by the equation Calculate the slope using the table. Graph y = -3 without using a table of values. the equation of a line is.

10 Graph x = 2 One of the variables has to be picked randomly, and the other is determined by the equation. for the equation x=2, which variable can be picked randomly and which is set by an equation? Calculate the slope using the table. the equation of a line is. Graph x = -2 without using a table of values. What is the pattern? y = 2x + 2 m = b = y = 2x + 1 m = b = y = -3x + 1 m = b = y = -3x - 1 m = b = These sets of lines are. In other words, they will go on forever but never meet. lines have the same. They do not need to have the same.

11 What is the pattern? y = 2x + 1 m = b = y = 1 x + 1 m = b = 2 y = -3x + 1 m = b = y = 1 x 2 m = b = 3 These sets of lines are. Such lines meet at an angle of 90 o. In other words, they will go on forever but never meet. lines have slope They do not need to have the same. Slopes of special cases Horizontal Lines Vertical Lines Point A (, ) Point B (, ) Point A (, ) Point B (, ) Slope = Slope =

12 4.5 Finding Equations of Special Cases Review Horizontal Line Vertical Line Parallel Lines Perpendicular Lines Graph: eq n slope notes Writing Equations of Special Cases Find the equation of a horizontal line with y-intercept of -2. Find the equation of a vertical line that passes through the point (-3, 5). Find the equation of the line that is parallel to y = 3x + 5 and passes through the point (-2, 4). Find the equation of the line that is perpendicular to y = -2x+3 and passes through the point (4, 5). Find the equation of the line that is parallel to y = 1 x - 2 and has an x-intercept of Find the equation of the line that is perpendicular y = 1x + 1 to and has a y-intercept of 5. 3