Questions and Answers
Write an equation in point-slope form for the points (1/2, 2/3) and (-3/2, 5/3).
y - 2/3 = -1/2(x - 1/2)
Write an equation in standard form for the slope 2/5 and the point (-1, 3).
y - 2/5x = 3.4
Find the slope and intercepts of the line f(x) = 4/5x + 7.
x intercept = -35/4, 0 ; y intercept = 0, 7
Write an equation for the line that goes through (-1, 3) and is parallel to y = 2x + 1.
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Write an equation for the line that goes through (-3, 4) and is vertical.
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What is the cost to produce 12 units if the cost of producing 4 units is $204.80 and the cost of producing 8 units is $209.60?
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How many subscribers will there be after 10 months if there were 5730 subscribers after 5 months and 6022 after 7 months?
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Is the set {(1,-2), (2, 3/4), (3, 3 + 1/2), (5, 9)} a function or relation?
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Is the set {(0.5, -1), (0.5, 0), (0.5, 1), (0.5, 3)} a function or relation?
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Is the set {(-3, 5), (0, -2), (0, 4), (1, -2)} a function or relation?
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For the function f(x) = 5x + 2, find f(-2), f(3), f(7).
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For the function f(x) = -1/3x + 1, find f(-2), f(3), f(7).
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For the function f(x) = -3x + 1.8, find f(-2), f(3), f(7), f(-1/2).
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What is g(-2)/f(3) if f(x) = -3x + 2 and g(x) = 1/2x - 1?
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What does a DOTTED line mean when graphing two-variable inequalities?
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What does a SOLID line mean when graphing two-variable inequalities?
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Find the slope of the line through the points (2, 3) and (-5, -9).
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Solve for y, slope (m), and y-intercept (b) in the equation 8x - 2y = 9.
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Study Notes
Point-Slope and Standard Form Equations
- Point-slope form equation derived from points (1/2, 2/3) and (-3/2, 5/3) is y - 2/3 = -1/2(x - 1/2)
- Standard form for a line with slope 2/5 through the point (-1, 3) simplifies to y - 2/5x = 3.4.
Slope and Intercepts
- For the linear function f(x) = 4/5x + 7:
- x-intercept is (-35/4, 0)
- y-intercept is (0, 7).
Parallel and Vertical Lines
- An equation for a line parallel to y = 2x + 1 through (-1, 3) is y = 2x + 5.
- A vertical line through (-3, 4) is represented as x = -3 (undefined slope).
Cost Calculations
- Cost of producing 12 units after producing 4 units for $204.80 and 8 units for $209.60 is $214.4.
Subscriber Growth
- Subscribers increased from 5730 after 5 months to 6022 after 7 months. The projection for 10 months is 6460 subscribers.
Functions vs. Relations
- Set { (1, -2), (2, 3/4), (3, 3+1/2), (5, 9) } is categorized as a Function.
- Set { (0.5, -1), (0.5, 0), (0.5, 1), (0.5, 3) } is categorized as a Relation due to repeating x-values.
- Set { (-3, 5), (0, -2), (0, 4), (1, -2) } is categorized as a Relation for the same reason.
Function Evaluations
- For the function f(x) = 5x + 2:
- f(-2) = -8, f(3) = 17, f(7) = 37 gives pairs (-2, -8), (3, 17), (7, 37).
- For f(x) = -1/3x + 1:
- Evaluations yield f(-2) = 5/3, f(3) = 0, f(7) = -4/3 resulting in (-2, 5/3), (3, 0), (7, -4/3).
- For f(x) = -3x + 1.8:
- Calculated values provide (-2, 7.8), (3, -7.2), (7, -19.2), (-1/2, 3.3).
Composite Functions
- For functions f(x) = -3x + 2 and g(x) = 1/2x - 1, calculating g(-2) / f(3) yields 2/7.
Graphing Inequalities
- A DOTTED line in graphing two-variable inequalities indicates relationships of less than or greater than.
- A SOLID line indicates relationships of less than or equal to, or greater than or equal to.
Slope Calculation
- Calculating slope between points (2, 3) and (-5, -9) yields a slope of 12/7.
Rearranging Linear Equations
- Rearranging the equation 8x - 2y = 9 results in the slope-intercept form y = 4x - 3, with slope m = 4 and y-intercept b = -3.
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Description
Test your understanding of key concepts from Algebra 2 through challenging problems on point-slope and standard form equations. This quiz covers various aspects including finding slopes and intercepts of lines. Perfect for revision or self-assessment!
