Podcast
Questions and Answers
Which equation represents the line passing through points A(4,7) and B(8,-5)? Assume the desired line is parallel to line AB.
Which equation represents the line passing through points A(4,7) and B(8,-5)? Assume the desired line is parallel to line AB.
- $y = \frac{1}{3}x - 2$
- $y = -3x - 2$
- $y = 3x - 7$
- $y = -3x + 5$ (correct)
For the line $y = -\frac{1}{4}x - 3$, which of the following represents the correct slope?
For the line $y = -\frac{1}{4}x - 3$, which of the following represents the correct slope?
- $-\frac{1}{4}$ (correct)
- $-\frac{3}{1}$
- $-\frac{1}{-4}$
- $\frac{3}{-1}$
Which of the following is not true about the line $y = 3x + 4$?
Which of the following is not true about the line $y = 3x + 4$?
- The y-intercept is 4.
- For every 1 unit that y increases, x increases by 3. (correct)
- For every 1 unit that x increases, y increases by 3.
- For every 1 unit that x decreases, y decreases by 3.
Given a proportional relationship where $x = 8$ and $y = -6$, which equation describes this relationship?
Given a proportional relationship where $x = 8$ and $y = -6$, which equation describes this relationship?
Which point is a solution to the system of equations $y = 3x + 8$ and $y = -2x - 22$?
Which point is a solution to the system of equations $y = 3x + 8$ and $y = -2x - 22$?
The equation of a line with a slope of 0 is always a vertical line.
The equation of a line with a slope of 0 is always a vertical line.
Parallel lines always have the same y-intercept.
Parallel lines always have the same y-intercept.
If a line passes through points (0, 5) and (3, 11), what is the value of y when x = 10?
If a line passes through points (0, 5) and (3, 11), what is the value of y when x = 10?
Give the equation of the line with a slope of $\frac{1}{2}$ that passes through point (-4, 5).
Give the equation of the line with a slope of $\frac{1}{2}$ that passes through point (-4, 5).
The intercept of a line is the point where the line crosses the ______-axis.
The intercept of a line is the point where the line crosses the ______-axis.
If two lines are parallel, they have the same _, but different y-intercepts.
If two lines are parallel, they have the same _, but different y-intercepts.
Match the following equation types to their corresponding line slope characteristics:
Match the following equation types to their corresponding line slope characteristics:
Which of the following lines, when graphed, would be the steepest?
Which of the following lines, when graphed, would be the steepest?
What is the slope of a line that passes through the points (-3, 11) and (6, -4)?
What is the slope of a line that passes through the points (-3, 11) and (6, -4)?
If the equation $y=2x - 2$ and $y=-2x + 4$ are solved using substitution, at which step is the substitution property of equality used?
If the equation $y=2x - 2$ and $y=-2x + 4$ are solved using substitution, at which step is the substitution property of equality used?
Flashcards
Proportional Variables
Proportional Variables
Constants of proportionality are proportional if their ratios are constant.
Slope
Slope
The measure of the steepness of a line.
Slope
Slope
The "m" in y = mx + b
Y-intercept
Y-intercept
Signup and view all the flashcards
Solving Systems Graphically
Solving Systems Graphically
Signup and view all the flashcards
Parallel Lines
Parallel Lines
Signup and view all the flashcards
Substitution
Substitution
Signup and view all the flashcards
Point of Intersection
Point of Intersection
Signup and view all the flashcards
Proportional Relationship
Proportional Relationship
Signup and view all the flashcards
Y-intercept
Y-intercept
Signup and view all the flashcards
Slope-intercept Form
Slope-intercept Form
Signup and view all the flashcards
System of Equations
System of Equations
Signup and view all the flashcards
Study Notes
- This is a review of equations of lines
- The review includes fluency skills, multiple choice, and free response questions
Fluency Skills
- For proportional variables, an equation for y in terms of x needs to be given
- If x=4 and y=28, then y=7x
- If x=48 and y=24, then y=0.5x
- If x=14 and y=21, then y=1.5x
- Lines to be graphed and labeled on a coordinate plane include:
- y=(4/5)x
- y=(3/2)x-6
- y=-4x+7
- y=2x-4
- y=-x-1
- The slope of a line is the "rise over run"
- The slopes of lines a and b need to be stated according to this principle
- The slope of a line that passes through pairs of points can be given in simplest form
- For points (2,4) and (17,14), the slope is 2/3
- For points (5,8) and (1,0), the slope is 2
- For points (-2,6) and (8,4), the slope is -1/5
- Systems of equations can be solved graphically
- Need to solve the systems of equations y=(3/4)x-7 and y=-x+7
- Need to solve the systems of equations y=3x-3 and y=-(1/2)x+4
- A system of equations can be solved algebraically
- Need to solve the system of equations y=6x+9 and y=2x-11
Multiple Choice Practice
- With a proportional relationship where x=8 and y=-6, one of the equations that describes it is y=-(3/4)x
- When graphed, the steepest line out of the following is y=(10/9)x
- The slope of a line that passes through the points (-3,11) and (6,-4) is -(5/3)
- For the line y=3x+4, it is not true that for every 1 unit that y increases, x increases by 3
- For the line y=-(1/4)x-3, a correct expression for the slope is (-1/4)
- The graph that represents the line y=2x-5 includes the point (0,-5) and (1, -3)
- A solution to the system y=3x+8 and y=-2x-22 is (-6, -10)
- To solve the system y=2x-2 and y=-2x+4, the substitution property of equality is used in Step 1 and Step 5
- For line AB passing through points A(4,7) and B(8,-5), the equation of a parallel line is y=-3x+5
- With values for points on a line being (-5, -13), (-2,-1), (1, 11), and (4, 23), the y-intercept of the line is -5
- A line passes through points (0,5) and (3,11); when this line passes through x=10, the value of y is 25
Free Response Practice
- A proportional relationship exists between x and y when x=9 and y=15
- An equation for y in terms of x expressed in simplest form needs to be written and the relationship graphed
- Whether the graph of this relationship be more or less steep that one whose equation is y = 2x needs to be determined
- A proportional relationship between x and y exists whose slope is 2/3
- The equation of this relationship in terms of x and y needs to be written
- With a point lying on this relationship whose y-coordinate is 14, what the x-coordinate is should be justified
- For a given plotted line a:
- The slope and y-intercept needs to be determined
- The equation of the line should be written
- Whether the points (8,4) and (4,5) lie on this line should be determined
- For the line y=-3x+1
- The slope of this line needs to be determined
- How to graph this line needs to be stated
- The graphed line needs to be shown
- A line has a slope of 1/2 and passes through the point (-4, 5)
- This line needs to be plotted on a grid and its equation written
- If this line contains the point (16, -5) should be justified
- y=-x+4 and y=-4x-2 needs to be solved algebraically and the answer verified graphically
- The lines v, w, x, and y need to be graphed and labeled
- Which lines make systems with solutions at (-2, 0) and (1, 6) needs to be determined
- Which of the lines form a system with no solutions needs to be determined
- Consider four lines:
- y=-(1/2)x+6
- y=-(3/4)x+6
- y=-(1/2)x-4
- y=-(3/4)x-4
- These lines should be plotted on a grid and the enclosed area shaded
- What kind of shape was shaded should be stated
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
