Podcast
Questions and Answers
Is the ordered pair (2, -4/5) a solution of the equation $5x + 3y = 2$?
Is the ordered pair (2, -4/5) a solution of the equation $5x + 3y = 2$?
False (B)
What is the x-intercept of the equation $4x + 5y = 8$?
What is the x-intercept of the equation $4x + 5y = 8$?
x = 2
What is the y-intercept of the equation $7 - 12x = 3y$?
What is the y-intercept of the equation $7 - 12x = 3y$?
y = 7/3
What is the slope of the line passing through the points (-10, -7) and (1, -2)?
What is the slope of the line passing through the points (-10, -7) and (1, -2)?
What is the value of y for the line passing through the points (6, y) and (3, 3) with slope $m = 2/3$?
What is the value of y for the line passing through the points (6, y) and (3, 3) with slope $m = 2/3$?
What is the average rate of change (slope) of the software company's profit from 1999 to 2005?
What is the average rate of change (slope) of the software company's profit from 1999 to 2005?
What is the equation relating x and y if they vary directly and x = -6, y = 42?
What is the equation relating x and y if they vary directly and x = -6, y = 42?
Which of the following are conditions for direct variation? (Select all that apply)
Which of the following are conditions for direct variation? (Select all that apply)
Are the graphs of the functions $f(x) = 3x + 2$ and $f(x) = rac{1}{3}x + 4$ parallel?
Are the graphs of the functions $f(x) = 3x + 2$ and $f(x) = rac{1}{3}x + 4$ parallel?
What is the value of the function $f(x) = -7x - 3$ at $x = -17$?
What is the value of the function $f(x) = -7x - 3$ at $x = -17$?
Flashcards
What is an x-intercept?
What is an x-intercept?
The x-intercept is the point where a line crosses the x-axis, found by setting y = 0 in the equation.
What is a y-intercept?
What is a y-intercept?
The y-intercept is the point where a line crosses the y-axis, found by setting x = 0 in the equation.
What is slope?
What is slope?
The slope (m) of a line measures its steepness and direction, calculated as the change in y divided by the change in x.
What is direct variation?
What is direct variation?
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Direct variation condition?
Direct variation condition?
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What does it mean for lines to be parallel?
What does it mean for lines to be parallel?
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How to evaluate a function?
How to evaluate a function?
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Study Notes
Ordered Pairs and Solutions
- An ordered pair (2, -4/5) does not satisfy the equation 5x + 3y = 2, leading to 7 3/5 ≠2.
Intercepts
- The x-intercept of the equation 4x + 5y = 8 is found at x = 2.
- The y-intercept of the equation 7 - 12x = 3y is y = 7/3.
Slope Calculation
- The slope (m) of the line through points (-10, -7) and (1, -2) is calculated as m = -5/11.
- To achieve a slope of 2/3 through the points (6, y) and (3, 3), the value of y must be 5.
Average Rate of Change
- From 1999 ($30 million profit) to 2005 ($210 million profit), the average rate of change in profit is $30 million per year, representing the linear growth over 6 years.
Direct Variation
- Direct variation between variables x and y can be described by the equation y = -7x, using the values x = -6 and y = 42 for derivation.
Conditions for Direct Variation
- For a relationship to be classified as direct variation, two conditions must be met:
- The y-intercept must be equal to 0.
- The graph of the function displays a straight line passing through the origin.
Parallel Lines Assessment
- The functions f(x) = 3x + 2 and f(x) = 1/3x + 4 do not represent parallel lines as their slopes differ.
Function Evaluation
- Evaluating the function f(x) = -7x - 3 at x = -17 results in an ordered pair (-17, 116).
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