Podcast
Questions and Answers
What is the slope of the line that passes through the points (2, -5) and (-3, y)?
What is the slope of the line that passes through the points (2, -5) and (-3, y)?
If a line has a slope of 3 and passes through the point (x, 8) and (2, 4), what is the value of x?
If a line has a slope of 3 and passes through the point (x, 8) and (2, 4), what is the value of x?
What is the slope of the line given by the equation y + 7 = \frac{1}{2}(x + 3)?
What is the slope of the line given by the equation y + 7 = \frac{1}{2}(x + 3)?
For the equation y = -6, what is the slope of the line?
For the equation y = -6, what is the slope of the line?
Signup and view all the answers
What is the slope of the line for the equation 5x - 4y = -20 when rewritten in slope-intercept form?
What is the slope of the line for the equation 5x - 4y = -20 when rewritten in slope-intercept form?
Signup and view all the answers
What is the slope of the line represented by the equation y = 2x - 4?
What is the slope of the line represented by the equation y = 2x - 4?
Signup and view all the answers
What can be concluded about lines with equal slopes?
What can be concluded about lines with equal slopes?
Signup and view all the answers
What is the scuba diver’s rate of change in feet per second as he descends underwater?
What is the scuba diver’s rate of change in feet per second as he descends underwater?
Signup and view all the answers
If Emerson traveled 40 km in 2 hours and 100 km in 5 hours, what is his speed in km/h?
If Emerson traveled 40 km in 2 hours and 100 km in 5 hours, what is his speed in km/h?
Signup and view all the answers
What is the slope of the equation $y = -2x + 3$?
What is the slope of the equation $y = -2x + 3$?
Signup and view all the answers
If the line $y = -3x - 6$ is shifted up 4 units, what will be the new equation?
If the line $y = -3x - 6$ is shifted up 4 units, what will be the new equation?
Signup and view all the answers
If the equation $y = 3x + 5$ changes to $y = 3x + 3$, how does the line graph change?
If the equation $y = 3x + 5$ changes to $y = 3x + 3$, how does the line graph change?
Signup and view all the answers
What type of slope does the line passing through the point (4, 7) have if it has an undefined slope?
What type of slope does the line passing through the point (4, 7) have if it has an undefined slope?
Signup and view all the answers
How would you express a line with no slope passing through (-5, -2) in slope-intercept form?
How would you express a line with no slope passing through (-5, -2) in slope-intercept form?
Signup and view all the answers
What is the equation of the line in slope-intercept form that passes through the points (-4, -5) and (11, 5)?
What is the equation of the line in slope-intercept form that passes through the points (-4, -5) and (11, 5)?
Signup and view all the answers
What is the x-intercept of the equation $6x - 9y = -36$?
What is the x-intercept of the equation $6x - 9y = -36$?
Signup and view all the answers
Which of the following is the correct slope-intercept form of a line parallel to $y - 8 = -\frac{1}{5}(x - 7)$ that passes through the point (-5, 3)?
Which of the following is the correct slope-intercept form of a line parallel to $y - 8 = -\frac{1}{5}(x - 7)$ that passes through the point (-5, 3)?
Signup and view all the answers
What is the correct equation in standard form for the line represented by $y - 5 = (x + 4)/2$?
What is the correct equation in standard form for the line represented by $y - 5 = (x + 4)/2$?
Signup and view all the answers
When transforming the equation $\frac{7}{2}x - 5 = y$ into standard form, which of the following represents the correct form?
When transforming the equation $\frac{7}{2}x - 5 = y$ into standard form, which of the following represents the correct form?
Signup and view all the answers
Which of the following represents the coordinates of the x-intercept of the equation in standard form $2y - 7x = -10$?
Which of the following represents the coordinates of the x-intercept of the equation in standard form $2y - 7x = -10$?
Signup and view all the answers
What is the coordinates of the y-intercept of the equation $7x - 2y = 10$?
What is the coordinates of the y-intercept of the equation $7x - 2y = 10$?
Signup and view all the answers
Which equation represents a line that is perpendicular to the line described by $y = -\frac{2}{5}x + 8$?
Which equation represents a line that is perpendicular to the line described by $y = -\frac{2}{5}x + 8$?
Signup and view all the answers
What is the slope of the line given by the equation $x - 4y = 16$?
What is the slope of the line given by the equation $x - 4y = 16$?
Signup and view all the answers
If a line is perpendicular to the line represented by $x - 4y = 16$, what should be the slope of the perpendicular line?
If a line is perpendicular to the line represented by $x - 4y = 16$, what should be the slope of the perpendicular line?
Signup and view all the answers
Which form of the equation is appropriate for writing the equation of a line given a point and a slope?
Which form of the equation is appropriate for writing the equation of a line given a point and a slope?
Signup and view all the answers
What is the general representation of a line parallel to one given by the point (1, -3) with a slope of 4 in Slope-Intercept form?
What is the general representation of a line parallel to one given by the point (1, -3) with a slope of 4 in Slope-Intercept form?
Signup and view all the answers
If two lines have slopes of $m_1$ and $m_2$, what condition must be met for them to be parallel?
If two lines have slopes of $m_1$ and $m_2$, what condition must be met for them to be parallel?
Signup and view all the answers
What is the equation of a line in Point-Slope Form that passes through the points (-4, 2) and (-8, -1)?
What is the equation of a line in Point-Slope Form that passes through the points (-4, 2) and (-8, -1)?
Signup and view all the answers
Which term best completes the statement: The lines are ______________ because their slopes are __________ _________.
Which term best completes the statement: The lines are ______________ because their slopes are __________ _________.
Signup and view all the answers
In the context of linear equations, if two lines are neither parallel nor perpendicular, what can you say about their slopes?
In the context of linear equations, if two lines are neither parallel nor perpendicular, what can you say about their slopes?
Signup and view all the answers
Study Notes
Unit 4 Study Guide: Linear Equations
- Instructions: Solve all problems algebraically, showing all work. Use simplified fractions (proper or improper) and use formative to check work. Do not use Desmos.
- Problem Solving: All work must be shown. Solve slope problems algebraically unless otherwise directed. Formative will be used to check progress, but only the work presented on this paper will be graded.
- Graphing tools: Graphing calculators may be used but not Desmos.
- Due date: Study guide is due at 8:00 am on the test date.
Slope Problems
- Question 1: Find the slope of the line that passes through (-6, -2) and (-6, 4).
- Question 2: Find the slope of the line passing through (4, -3) and (-12, 7).
- Question 3: Identify the slope of the line: y + 7 = ⅓(x + 3)
- Question 4: Identify the slope of the line: y = -6
- Question 5: Solve for the slope in the equation 5x - 4y = -20
- Question 6: A line with a slope of 3 passes through (2, -5) and (-3, y). Find the missing y-value.
- Question 7: A line with a slope of passes through (x, 8) and (2, 4). Find the missing x-value.
Writing the Equation of a Line
- Question 8: Determine the slope of the given line and justify your answer with work on the graph
- Question 9: Graph the given liner equation.
- Question 10: A scuba diver is 30 feet below the surface after 10 seconds, and 100 feet below after 40 seconds. Find the scuba diver's rate of change.
- Question 11: After 2 hours of biking, Emerson has traveled 40 km. After 5 hours, he has traveled 100 km. Find the rate at which he bikes.
- Question 12: Solve for the equation of a line: y = 2x - 4
- Question 13: Identify the equation of a line: y = -6
- Question 14: Find the equation of a line: -2x + 3y = 12
- Question 15: Find the equation of a line: y - 5 = ½ (x + 4)
Transformations
- Question 16: The graph of y = -3x - 6 is shown. If the line is shifted up 4 units and is twice as steep. What is the new equation?
- Question 17: Trevor graphed the line y = 3x + 5. If the 5 changes to a 3, how will the line graph change? (options: moves up/down, rises less/more steeply)
- Question 18: Find a linear equation with no slope that passes through the point (-5, -2).
- Question 19: Find an equation of a line with an undefined slope and passing through (4, 7).
- Question 20: Write the equation of the line from the graph (in slope-intercept form) showing all work algebraically.
- Question 21: Write an equation in slope-intercept form for the line with slope m = ⅔ and passes through the point (6, -5)
- Question 22: Write an equation in slope-intercept form that passes through points (-4, -5) and (11, 5).
Standard Form Equations
- 23 & 24: Find the x- and y-intercepts for the equation 6x - 9y = -36. Express these as ordered pairs.
- 25: Graph the equation from Question 23.
- 26: Simplify -x/2 - 5 = y into standard form (integer coefficients, positive leading coefficient).
- 27: Simplify the equation into standard form (with integers and positive leading coefficients). Write the x and y intercepts as ordered pairs.
- 28 & 29: Find the x and y-intercepts for the simplified equation in Question 27. Write these as ordered pairs.
Parallel & Perpendicular Lines
- Question 30: Write an equation in slope-intercept form of a line that passes through (-5, 3) and is parallel to y - 8 = (-2/7)(x - 7)
- Question 31: Write the equation in slope-intercept form of the line that passes through (8, 2) and is perpendicular to x - 4y = 16.
Graphing & Equations
-
Questions 32 & 33: Write the equation in slope-intercept form.
- Question 32: Passes through (1, -3) and is parallel to y + 2 = 4(x - 1).
- Question 33: Passes through (6, -4) and is perpendicular to y = 4x
- Question 34-36: Use the graph to write the equations in slope-intercept or slope-point form.
- Question 37: Determine if the lines are parallel, perpendicular, or neither. Compare the slopes.
- Question 38: Determine if the equations are parallel, perpendicular, or neither. Show your work algebraically.
- Question 39: Write the equation in slope-point form that passes through points (-4, 2) and (-8, -1).
- Question 40: Write a linear equation in slope-intercept form to model the situation. Alex and Steve participated in a fundraiser. Alex raised $39.75 for 25 laps and Steve raised $32.25 for 19 laps. Find a formula for the amount raised as a function of the number of laps.
- Question 41: Based on question 40, what was the flat rate that each friend received as part of the pledges?
- Question 42: Based on question 40, how much would a participant raise if they walked 12 laps?
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Related Documents
Description
Test your knowledge on calculating slopes of lines and understanding rates of change. This quiz includes various scenarios including points, equations, and real-world speed calculations. Challenge yourself with different types of slope problems and see how well you understand this fundamental concept in mathematics.
