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Questions and Answers
In the linear equation $y = \frac{3}{4}x - 1$, what is the slope?
In the linear equation $y = \frac{3}{4}x - 1$, what is the slope?
m = \frac{3}{4}
What is the slope of a horizontal line?
What is the slope of a horizontal line?
m = 0
What is the slope of a vertical line?
What is the slope of a vertical line?
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What is the slope of a line that contains the points $(-6, 1)$ and $(4, -4)$?
What is the slope of a line that contains the points $(-6, 1)$ and $(4, -4)$?
What is the slope of the line whose equation is $2y = 3x + 4$?
What is the slope of the line whose equation is $2y = 3x + 4$?
Convert the equation $x - 4y = 8$ to slope-intercept form.
Convert the equation $x - 4y = 8$ to slope-intercept form.
What is the x-intercept of the equation $10x + 4y = -20$?
What is the x-intercept of the equation $10x + 4y = -20$?
What is the y-intercept of the equation $10x + 4y = -20$?
What is the y-intercept of the equation $10x + 4y = -20$?
What type of line is formed by the equation $y = -2$?
What type of line is formed by the equation $y = -2$?
What type of line is formed by the equation $x = 7$?
What type of line is formed by the equation $x = 7$?
Write the slope-intercept form equation for the line that passes through the point $(2, -1)$ and has a slope of -3.
Write the slope-intercept form equation for the line that passes through the point $(2, -1)$ and has a slope of -3.
Write the slope-intercept form equation for the line that passes through the point $(-4, -9)$ and has a slope of $\frac{1}{2}$.
Write the slope-intercept form equation for the line that passes through the point $(-4, -9)$ and has a slope of $\frac{1}{2}$.
Write the slope-intercept form equation for the line that passes through the points $(-4, 3)$ and $(2, -6)$?
Write the slope-intercept form equation for the line that passes through the points $(-4, 3)$ and $(2, -6)$?
What is the equation of the line that passes through the points $(-4, 8)$ and $(1, 3)$?
What is the equation of the line that passes through the points $(-4, 8)$ and $(1, 3)$?
What is the slope of a line parallel to the line $4x + y = 5$?
What is the slope of a line parallel to the line $4x + y = 5$?
Which of the following equations represents a line parallel to the y-axis? $y = x$ OR $x = 4$ OR $y = 4$ OR $y = x + 4$
Which of the following equations represents a line parallel to the y-axis? $y = x$ OR $x = 4$ OR $y = 4$ OR $y = x + 4$
Which of the following equations represents a line perpendicular to the y-axis? $y = x$ OR $x = 4$ OR $y = 4$ OR $y = x + 4$
Which of the following equations represents a line perpendicular to the y-axis? $y = x$ OR $x = 4$ OR $y = 4$ OR $y = x + 4$
What is the slope of a line perpendicular to the line $5x - 3y = 27$?
What is the slope of a line perpendicular to the line $5x - 3y = 27$?
What is the slope of a line that passes through the point $(3, -1)$ and is perpendicular to the line with an equation $y = -3x + 8$?
What is the slope of a line that passes through the point $(3, -1)$ and is perpendicular to the line with an equation $y = -3x + 8$?
Using the line of best fit, which is closest to the length of time it should take Marsha's 8-year-old son to run one lap?
Using the line of best fit, which is closest to the length of time it should take Marsha's 8-year-old son to run one lap?
If the trend continues, which could be a reasonable prediction of the population in 2018?
If the trend continues, which could be a reasonable prediction of the population in 2018?
Write and solve a linear equation to find the total cost to rent the snowboard from 8:30 a.m. to 12:30 p.m., given the resort charges $15.75 per hour in addition to a $25 deposit.
Write and solve a linear equation to find the total cost to rent the snowboard from 8:30 a.m. to 12:30 p.m., given the resort charges $15.75 per hour in addition to a $25 deposit.
Write and solve a linear equation to find the cost to rent the shoes if Brandon played 5 games and paid $32 at $4.95 per game.
Write and solve a linear equation to find the cost to rent the shoes if Brandon played 5 games and paid $32 at $4.95 per game.
Write and solve a linear equation to find the monthly rent for a 1500 square foot office, given the rent for an 800 square foot office is $975 and for an 1100 square foot office is $1125.
Write and solve a linear equation to find the monthly rent for a 1500 square foot office, given the rent for an 800 square foot office is $975 and for an 1100 square foot office is $1125.
If Brielle has 66 nickels and the total value in her piggy bank is $7.80, write and solve a linear equation to find the number of dimes she has.
If Brielle has 66 nickels and the total value in her piggy bank is $7.80, write and solve a linear equation to find the number of dimes she has.
Direct, Inverse or Neither: $\frac{y}{3} = x$?
Direct, Inverse or Neither: $\frac{y}{3} = x$?
Direct, Inverse or Neither: $xy = 40$?
Direct, Inverse or Neither: $xy = 40$?
Direct, Inverse or Neither: $8x - 2y = 2$?
Direct, Inverse or Neither: $8x - 2y = 2$?
If the point $(2, -10)$ lies on the graph of an inverse variation, what is the constant of variation?
If the point $(2, -10)$ lies on the graph of an inverse variation, what is the constant of variation?
If the point $(12, 4)$ lies on the graph of a direct variation, what is the constant of variation?
If the point $(12, 4)$ lies on the graph of a direct variation, what is the constant of variation?
If $y$ varies directly as $x$ and $y = 3$ when $x = 12$, what is the value of $y$ when $x = 18$?
If $y$ varies directly as $x$ and $y = 3$ when $x = 12$, what is the value of $y$ when $x = 18$?
Flashcards
What is slope?
What is slope?
The rate of change of a line; rise over run.
Slope of a horizontal line?
Slope of a horizontal line?
A line that runs horizontally has zero steepness.
Slope of a vertical line?
Slope of a vertical line?
A line that runs vertically has an undefined steepness, as run is zero.
What is y = mx + b?
What is y = mx + b?
Slope-intercept form of a linear equation, where m is the slope and b is the y-intercept.
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What is the x-intercept?
What is the x-intercept?
The point where the line crosses the x-axis.
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What is the y-intercept?
What is the y-intercept?
The point where the line crosses the y-axis.
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What is a horizontal line?
What is a horizontal line?
A line with a constant y-value.
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What is a vertical line?
What is a vertical line?
A line with a constant x-value.
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What are parallel lines?
What are parallel lines?
Lines that never intersect and have the same slope.
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What are perpendicular lines?
What are perpendicular lines?
Lines that intersect at a right angle; their slopes are negative reciprocals.
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What is direct variation?
What is direct variation?
A relationship where one variable increases as the other increases.
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What is inverse variation?
What is inverse variation?
A relationship where one variable increases as the other decreases.
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What is the constant of variation?
What is the constant of variation?
The constant 'k' in direct/inverse variation equations.
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Slope and Line Types
- Slope of the line in the equation y = 3/4x - 1 is m = 3/4.
- Horizontal lines have a slope of m = 0.
- Vertical lines have an undefined slope.
- Slope between points (-6, 1) and (4, -4) is m = -1/2.
- Line described by 2y = 3x + 4 has a slope m = 3/2.
Slope-Intercept Form
- Convert line x - 4y = 8 to slope-intercept form: y = 1/4x - 2.
- Line that passes through (2, -1) with slope -3 is: y = -3x + 5.
- Line passing through (-4, -9) with a slope of 1/2 is: y = 1/2x - 7.
- Line through points (-4, 3) and (2, -6) results in slope-intercept form: y = -3/2x - 3.
- Equation of line through points (-4, 8) and (1, 3) is: y = -x + 4.
Parallel and Perpendicular Slopes
- Slope of a line parallel to 4x + y = 5 is m = -4.
- Equation x = 4 represents a line parallel to the y-axis.
- Equation y = 4 represents a line perpendicular to the y-axis.
- Slope of line perpendicular to 5x - 3y = 27 is m = -3/5.
- Slope of line through (3, -1) perpendicular to y = -3x + 8 is m = 1/3.
Graphing and Predictions
- Based on time and age data, a prediction for an 8-year-old's time to run a lap is 176 seconds.
- From provided population data, reasonable prediction for Virginia's population in 2018 is 8.72 million.
Linear Equations and Costs
- Total cost for snowboard rental from 8:30 a.m. to 12:30 p.m. is $88.
- Cost calculation for bowling shoes where Brandon played 5 games and paid $32 results in a shoe rental cost of $7.25.
- Monthly rent for a 1500 square foot office is predicted to be $1325.
Word Problems and Equations
- Brielle has a total of $7.80 with 66 nickels, leading to 45 dimes.
- Identifying types of variation: y/3 = x is a Direct variation; xy = 40 is Inverse; and 8x - 2y = 2 is Neither variation.
- Inverse variation constant k for point (2, -10) is k = -20.
- Direct variation constant k for point (12, 4) is k = 1/3.
- When y varies directly as x, with y = 3 when x = 12, the value of y when x = 18 is 4.5.
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