Unit 4 Study Guide: Linear Equations
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Questions and Answers

What is the slope of the line that passes through the points (2, -5) and (-3, y)?

  • -1
  • 1
  • 0
  • -2 (correct)

    • Find the slope of the line that passes through the points (4, -3) and (-12, 7).

  • -5/8
  • 5/8
  • -5/4 (correct)
  • 5/4

    • What is the y-value for the point (-6, y) on the line with a slope of 3 passing through point (2, -5)?

  • 3
  • -2
  • 2
  • 1 (correct)

    • Identify the slope of the given line: y + 7 = (1/2)(x + 3).

    <p>1/2</p> Signup and view all the answers

    What is the slope of the line represented by the equation y = -6?

    <p>0</p> Signup and view all the answers

    Which of the following equations has a slope of 3?

    <p>y = 3x + 4</p> Signup and view all the answers

    How would you find the missing x-value for the points (x, 8) and (2, 4) on a line with a slope of 1/2?

    <p>Set the slope equal to 1/2 and use the y-values.</p> Signup and view all the answers

    What can you conclude about the line represented by the equation 5x - 4y = -20?

    <p>It has a slope of -5/4.</p> Signup and view all the answers

    What type of line is represented by the equation $x - 4y = 16$?

    <p>Oblique line</p> Signup and view all the answers

    What is the slope of the line represented by the equation $y + 2 = 4(x - 1)$?

    <p>4</p> Signup and view all the answers

    If a line is perpendicular to $x - 4y = 16$, what is the slope of that line?

    <p>-4</p> Signup and view all the answers

    Which form is used to write the equation of a line that passes through a given point and has a specific slope?

    <p>Point-slope form</p> Signup and view all the answers

    When determining whether two lines are parallel, what aspect do you primarily compare?

    <p>Slopes</p> Signup and view all the answers

    Which equations represent parallel lines?

    <p>$y = 3x + 1$ and $y = 3x + 9$</p> Signup and view all the answers

    What is the general relation of the slopes of two lines if they are perpendicular?

    <p>They are negative reciprocals.</p> Signup and view all the answers

    In order to express the equation of a line in slope-intercept form, which information must you have?

    <p>A point and a slope</p> Signup and view all the answers

    What is the scuba diver’s rate of change in depth per second?

    <p>3 feet per second</p> Signup and view all the answers

    If Emerson biked 40 km in 2 hours and 100 km in 5 hours, what is his average speed in km/h?

    <p>25 km/h</p> Signup and view all the answers

    What is the new equation of the line after shifting the graph of y = -3x - 6 up by 4 units and doubling its steepness?

    <p>y = -6x - 2</p> Signup and view all the answers

    What happens to the graph of y = 3x + 5 if the constant term changes from 5 to 3?

    <p>The line moves down two units</p> Signup and view all the answers

    What is the equation of a line with no slope that passes through the point (-5, -2)?

    <p>y = -2</p> Signup and view all the answers

    What is the equation of a line with an undefined slope that passes through the point (4, 7)?

    <p>x = 4</p> Signup and view all the answers

    Write the equation in slope-intercept form for the line that passes through the points (-4, -5) and (11, 5). What is the slope?

    <p>y = (10/15)x - 5</p> Signup and view all the answers

    What is the transformation of the line represented by the equation -2x + 3y = 12 if it is rewritten in slope-intercept form?

    <p>y = (2/3)x + 4</p> Signup and view all the answers

    What is the x-intercept of the equation $6x - 9y = -36$?

    <p>(6, 0)</p> Signup and view all the answers

    Which equation is in slope-intercept form for a line parallel to $y - 8 = -\frac{1}{5}(x - 7)$ and passes through the point (-5, 3)?

    <p>$y = -\frac{1}{5}x + 2$</p> Signup and view all the answers

    Which of the following is the correct integer form of the equation $\frac{7}{2}x - 5 = y$?

    <p>$7x - 10 = 2y$</p> Signup and view all the answers

    The slope of a line parallel to $y = 2x + 3$ is:

    <p>2</p> Signup and view all the answers

    What would be the slope of a line perpendicular to the equation $y = -\frac{3}{4}x + 1$?

    <p>\frac{4}{3}</p> Signup and view all the answers

    For the equation $9y - 5 = 2(x + 4)$, which of the following represents the y-intercept?

    <p>(0, 5)</p> Signup and view all the answers

    If an equation is written in standard form $Ax + By = C$, which of the following must be true?

    <p>A must be non-negative.</p> Signup and view all the answers

    Study Notes

    Unit 4 Study Guide: Linear Equations

    • This guide covers linear equations, including slope, intercepts, graphing, transformations, and standard form.
    • All problems are to be completed algebraically, showing full work, and using simplified fractions (proper or improper format).
    • Formative assessments will check progress, and only the steps of work on this paper will be graded.
    • A copy of the study guide must be turned in by 8:00 am on the test date.
    • All work for questions with slopes must be shown algebraically.

    Slope Problems

    • Question 1: Find the slope of a line passing through (-6, -2) and (-6, 4).
    • Question 2: Find the slope of a line passing through (4, -3) and (-12, 7).
    • Question 3: Identify the slope of the line: y + 7 = (1/3)(x + 3).
    • Question 4: The slope of the line is y = -6.
    • Question 5: Find the missing variable in the equation: 5x – 4y = -20.
    • Question 6: Find the missing y-value for a line with slope 3 passing through (2,-5) and (-3, y).
    • Question 7: Find the missing x-value for a line with a slope of ⁻¹/₂ passing through (x, 8) and (2, 4).

    Graphing Equations

    • Question 8: Determine the slope of a given line in a graph

    • Question 9: Graph a given linear equation.

    • Question 10: Find the rate of change for a scuba diver who is at certain depths at certain times during a dive.

    • Question 11: Calculate the rate of bike travel given travelled distances and times for Emerson.

    • Question 12: Graph the equation y = 2x-4.

    • Question 13: Graph the equation y = -6.

    • Question 14: Graph the equation -2x + 3y = 12.

    • Question 15: Graph the equation y - 5 = 1/2(x + 4).

    Transformations

    • Question 16: Find the equation of a line that's shifted up 4 units and is twice as steep as y = -3x-6.
    • Question 17: Describe how changing the constant in the equation y = 3x + 5 will affect the graph.
    • Question 18: Determine the equation of a line with no slope passing through a specific point.
    • Question 19: Determine the equation of a line with an undefined slope passing through a specific point.
    • Question 20: Find the equation of a line given a graph in slope-intercept form.

    Slope-Intercept Form

    • Question 21: Find the slope-intercept form equation of a line with a given slope and point.
    • Question 22: Find the slope-intercept form equation of a line using two points.
    • Question 23 -24: Determine x-intercept and y-intercept of the equation 6x – 9y = -36. Write answers as ordered pairs.
    • Question 25: Graph the equation of 6x - 9y = -36

    Standard Form Equations

    • Question 26: Convert the equation y − 8=⁻²⁄₃(x − 7) into standard form.
    • Question 27: Convert a provided equation to standard form with integer coefficients and positive leading coefficients
    • Question 28: Find the x-intercept of a provided standard form equation.
    • Question 29: Find the y-intercept of a provided standard form equation.

    Parallel and Perpendicular Lines

    • Question 30: Write the equation of the line that passes through a given point and is parallel to a given equation.
    • Question 31: Write the equation of the line that passes through (8, 2) and is perpendicular to x - 4y = 16.
    • Question 32: Write the equation of the line that passes through (1,-3) and is parallel to y + 2 = 4(x – 1).
    • Question 33: Write the equation of the line that passes through (6, -4) and is perpendicular to y = 4x.

    Graphing and Equations of Lines

    • Question 34: Write the equation of the line in point-slope form that passes through two given points on a graph.
    • Question 35: Write the equation of the line in point-slope form that passes through two given points on a graph.
    • Question 36: Use the provided graph for questions 34 -36.
    • Question 37: Determine whether two lines are parallel, perpendicular, or neither based on their slopes.
    • Question 38: Determine whether two lines are parallel, perpendicular, or neither based on their equations.

    Modeling Situations with Linear Equations

    • Question 39: Write the equation in point-slope form for a line that passes through two given points
    • Question 40: Write a linear equation to model a fundraiser situation given information on fundraising amounts based on laps run.
    • Questions 41-42: Answer questions based on a modelled fundraiser.

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    Related Documents

    Algebra 1 Honors Unit 4 Study Guide PDF 2022-2023

    Description

    This study guide focuses on linear equations including concepts like slope, intercepts, and graphing. The problems are designed to be solved algebraically with full work shown, emphasizing the understanding of linear transformations and standard form. Make sure to submit your completed guide by the deadline for assessment.

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