Graphing and Writing Linear Equations Review.1,., 4.1-4. & 4.4 Algebra I Name: Date: Period: Quest Topics Section.1 linear versus nonlinear rewrite linear equations in standard form: Ax By C find and use x and y intercepts to graph graph and write equations of horizontal and vertical lines word problems; write and graph linear equations and be able to interpret x and y intercepts Section. find and interpret rate of change from a table and a graph y y1 find the slope from a graph and/or given two points: m x x 1 find the missing coordinate when given slope and two points Sections 4.1-4. graph lines in slope intercept form: y mx b write equations in slope intercept form given: m and b, m and a point, two points, a graph rewrite linear equations in slope intercept form: y mx b Section 4.4 determine if a set of lines are parallel, perpendicular or neither write equations in slope intercept form given through a point and parallel or perpendicular to a line Directions: Read the directions carefully and show your step by step work. 1. Determine if the following equations are linear. If not, explain why not. a. y x 7. Write each equation in standard form: a. y = x b. x9y 4 x c. y d. x 1 b. y x 10 e. xy f. y x
. State the domain, range, slope and graph: x = 4. Find the x and y intercepts and graph: 10x y = 0 domain: x intercept: range: slope:. Pick-M-Up Towing Company charges $40 to hook a car and $1.70 for each mile that it is towed. The equation y = 1.7x + 40 represents the total cost y for x miles towed. Determine the y-intercept. Describe what the value means in this context. 6. Is the following linear? If so, find and interpret the rate of change. 7. State the slope and y intercept. 8. Find the slope through the points (0, 0) and ( 14, 1). slope:
9. Find the slope through the points (, ) and (, ). 4 10. Find the value of r, given a slope of r,1 and, r. and through the points 11. State the slope, y intercept, domain and range of y x. 1. State the slope and y intercept of x y = 6. slope: slope: domain: range: 1. State the slope, y intercept, domain and range of y. 14. Are the following parallel, perpendicular or neither? slope: a. 1 y x6 x y6 domain: range: b. y x6 4x6y4 c. x 9 y d. y x y x
1. Write an equation in slope intercept form with a slope and a y intercept of 1. 16. Write an equation in slope intercept form with a slope and through the point 10,. 17. Write an equation in slope intercept form with no slope and through the point, 4. 18. Write an equation in slope intercept form 1,4 and 0, 1. through the points 19. Write an equation in slope intercept form,4 and 7,4. through the points 0. Write an equation in slope intercept form through the point 1, and parallel to yx 4.
1. Write an equation in slope intercept form through the point 4,1 and perpendicular to y x 4.. Write an equation in slope intercept form through the point,1 and perpendicular to x 0.. Write an equation in slope intercept form with an x-intercept of 4 and y-intercept of. 4. Write an equation of a vertical line that passes through the point,10.. Write an equation of a horizontal line that passes through the point,10. 6. Are these two lines perpendicular? Justify your answer.
7. A certain car uses 1 gallons of gas in hours. If the rate of gasoline consumption is constant, how much gasoline will the car use on a hour trip? 8. The cost of the junior prom is $9 plus $1 for each person attending. a. Write an equation that gives total cost, y, as a function of the number of people attending, x. b. What is the cost for 7 people? 9. In 1980 the average price of a home in Green County was $97,000. By 1986 the average price of a home was $109,000. Write a linear model for the price of a home, y, in Geen County as a function of the year, x. [Hint ~ let x = 0 correspond to 1980] 0. A daily newspaper had 1,1 subscribers when it began publication. Five years later it had 10,100 subscribers. What is the average yearly rate of change in the number of subscribers for the five-year period? 1. Determine whether the function is linear. Write linear or not linear. x y 0 1 1 4 1
ANSWER KEY 1. a. linear b. linear c. nonlinear, exponential function d. linear e. nonlinear, product of variables/ nd degree f. nonlinear, quadratic function. a. xy 10 b. xy. x y domain: range: no slope 4.,0 ; 0,4. the y intercept is 40, which is the fee to hook the car 6. yes; the pool lost gallons of water per minute m and 0,0 8. 7. m 9. m undefined 10. r 11 11. m 1; 0,0 ; domain: x range: y ; 0, 1. m 1. m 0; 0, ; domain: x range: y 14. a. perpendicular b. parallel c. perpendicular d. neither 1. y x 1 16. y x 8 17. x 18. y x 1 19. y 4 0. y x 1. 1 y x 1. y 1
. y x 4. x. y 10 4 6. Line A has a slope of 1 and line B has a slope of, since these slopes are negative reciprocals of each other, line A and line B are perpendicular to each other. 7. 17 gallons 8. a. y1x 9 b. $10.00 9. y000x 97000 0. 40 subscribers less per year 1. not linear