Algebra 1 Honors Unit 4 Study Guide PDF 2022-2023

NAME _____________________ UNIT 4 STUDY GUIDE Date __________ Period ____ Linear Equations Algebra 1 Honors DIRECTIONS: Complete all problems as directed showing the work algebraically like we have practiced...

NAME _____________________ UNIT 4 STUDY GUIDE Date __________ Period ____ Linear Equations Algebra 1 Honors DIRECTIONS: Complete all problems as directed showing the work algebraically like we have practiced this unit. If needed, write simplified fractions either in proper or improper format. Then enter your answers and work in FORMATIVE. You should re-do any incorrect problems on both your paper and in Formative until you earn 100%. This process will help you to focus on the areas that you need to review before the Test. Remember, you may NOT use DESMOS – but you can use a graphing calculator. While you will be entering your answers in FORMATIVE to check your progress, only the steps of your work on this paper copy will be graded. This study guide will be due at 8:00am on your test date: _____________. Solve each Slope problem as directed. Show work algebraically unless directed otherwise. Question 1 : Question 6 : What is the slope of the line that passes through the A line with a slope of 3 passes through two points, pair of points? (𝟐, −𝟓) and (−𝟑, 𝒚). Find the missing y-value. All (−𝟔, −𝟐), (−𝟔, 𝟒) work must be shown algebraically. Question 2 : Find the slope of a line that passes through (4, -3) and (-12, 7). Question 7 : A pair of points, (𝒙, 𝟖) and (𝟐, 𝟒) lie on a line with a 𝟏 Identify the slope of the line for each given slope of. Find the missing x-value. All work 𝟐 problem below. must be shown algebraically. 𝟑 Question 3: 𝒚+𝟕= (𝒙 + 𝟑) 𝟐 Question 4: 𝒚 = −𝟔 Question 5: 𝟓𝒙 − 𝟒𝒚 = −𝟐𝟎 UNIT 4 STUDY GUIDE Linear Equations Write the slope of the given line. Justify your Graph the equation of the given line. answer with work on the graph. Question 12: Question 8: Question 9: 𝒚 = 𝟐𝒙 − 𝟒 Question 13: 𝑚 = __________ 𝑚 = __________ 𝒚 = −𝟔 Finding the Rate of Change Write your answers as a short sentence. Question 10 : A scuba diver is 30 feet below the surface of the water after 10 seconds of jumping in and 100 feet below the surface after 40 seconds. What is the scuba diver’s rate of change? Question 14: −𝟐𝒙 + 𝟑𝒚 = 𝟏𝟐 Question 11: After 2 hours of biking, Emerson has traveled Question 15: 40 km. He traveled 100 km after 5 hours of biking. If he is able to maintain the same 𝟏 𝒚 − 𝟓 = − (𝒙 + 𝟒) speed throughout his day, what is the rate at 𝟐 which he bikes? UNIT 4 STUDY GUIDE Linear Equations Question 20: Transformations Write the equation of the line from the graph below in slope-intercept form. Show all work algebraically. Question 16: The graph of 𝑦 = −3𝑥 − 6 is shown. If the line in the graph is shifted up 4 units and is twice as steep, what is the equation of the new line in slope intercept form? _____________________________________ Question 17: Question 21: Trevor graphed the line 𝑦 = 3𝑥 + 5. If the 5 Write an equation in slope-intercept form for the line changes to a 3, how will the line graph change? that has the given slope, m, and passes through the given point. a) It will move up two b) It will move down two c) It rises less steeply d) It rises more steeply Slope-Intercept Form Question 18: Write the equation of a line with no slope and Question 22: passing through the point (-5, -2). Write an equation in slope-intercept form that passes through the points (-4, -5) and (11, 5). Question 19: Write the equation of a line with an undefined slope and passing through the point (4, 7). UNIT 4 STUDY GUIDE Linear Equations Question 27 Standard Form Equations Simplify the equation into Standard Form with For Questions 23-24, identify the x-intercept and integer coefficients. Leading coefficients should be the y-intercept for the equation 6𝑥 − 9𝑦 = −36. positive. Then for questions 28-29, write the x- Write your answers as ordered pairs. Then graph intercept and y-intercept of this standard form the equation for Question 25. equation as ordered pairs. 9 𝑦 − 5 = (𝑥 + 4) 2 Question 23) x-intercept: _______ Question 24) y-intercept: _______ Question 25) Question 28) x-intercept: ________ Question 29) y-intercept: ________ Parallel & Perpendicular Lines Question 30: Write an equation in Slope-Intercept form for the line that passes through (-5, 3) and is parallel to the following equation: 2 𝑦 − 8 = − (𝑥 − 7) 5 Question 26: 7 Simplify the equation 𝑥 − 5 = 𝑦 into Standard 2 Form with integer coefficients. Leading coefficients should be positive. UNIT 4 STUDY GUIDE Linear Equations Questions 34-36 : Question 31: Use the graph to answer Write an equation in slope-intercept form for the questions 34-36. Be sure line that passes through the given point (8, 2) to show work algebraically to justify and is perpendicular to the line 𝑥 − 4𝑦 = 16. your answer choices. 34) Write an equation of the line that passes through points A and D in Point-Slope Form. __________________________ Question 32 : 35) Write an equation of a line that passes through points B and C in Point-Slope form. Write an equation in Slope-Intercept form for the line that passes through (1,-3) and is parallel to 𝑦 + 2 = 4(𝑥 − 1) ___________________________________ Fill-in the blanks about how two lines above are related using our linear equations vocabulary: 36) The lines are ______________ because their slopes are __________ _________. Question 33: Write an equation for the line that passes through the following point and is perpendicular to the given line. UNIT 4 STUDY GUIDE Linear Equations Point-Slope Equation Question 37: Question 39: Determine whether the lines are parallel, Write an equation in point-slope form of the line perpendicular or neither. Show work by that passes through the points (-4,2) and (-8,-1) comparing the slopes of each line. The lines are ______________________. Question 40: Write a linear equation to model the situation in Slope-Intercept form. Be sure to show all work algebraically to justify your answer. Two friends, Alex and Steve, are participating in a fundraiser walk-a-thon for the local homeless Question 37: shelter. Each have gotten pledges that include the Determine whether the lines are parallel, same fixed amount of money for participating plus perpendicular or neither. Show work by an additional amount of money raised for each lap that they complete. For completing 19 laps, Steve comparing the slopes of each line. raised $32.25 and Alex raised $39.75 for completing The lines are ______________________. 25 laps. Questions 41-42: Question 38: Based on your result in QUESTION 40, answer the Are the equations parallel, perpendicular or following questions: neither? Show work algebraically to justify your answer choice. 41) What was the flat rate that each friend received as 1 part of their pledges? 2𝑥 + 8𝑦 = −12 𝑦 − 7 = − 4 (𝑥 − 2) 42) How much money would a participant in the walk-a-thon raise if they walked 12 laps? UNIT 4 STUDY GUIDE Linear Equations