Questions and Answers
If f(x) = 5x - 12, what is f(2)?
-2
What is the point where the cost c(x) = 2x + 2.00 at x = 0?
(0,2)
The slope of f(x) is the same as the slope of g(x) for the given functions.
True
What does the slope mean for the taxi ride cost c(x) = 2x + 3.00?
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What does the y-intercept mean in the context of Karma's birthday money equation y = 75x + 60?
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What is the y-intercept of the line given by the equation y = -10x + 14?
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What is the point that matches the graph of y = -2x - 3 at x = 1?
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The graph of y = -4x + 7 is a line that shows the set of all solutions to the equation.
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Which equation represents the temperature, t, at hour h, given the conditions?
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Study Notes
Slope Intercept Equation of a Line
- The function f(x) = 5x - 12 evaluated at x = 2 gives f(2) = -2.
- The cost function for a taxi ride is c(x) = 2x + 2.00, representing cost in dollars based on time in minutes, with a y-intercept at (0, 2).
- The slopes of the functions f(x) and g(x) = -2x - 5 are equivalent, indicating parallelism in their rate of change.
- In the taxi cost function c(x) = 2x + 3.00, the slope of $2.00 per minute describes how incremental time affects the fare.
- The y-intercept of the equation y = 75x + 60 represents Karma's initial birthday money of $60.
- The y-intercept of the equation y = -10x + 14 is (0, 14), indicating the point where the line crosses the y-axis.
- The line described by y = -2x - 3 reveals the set of all solutions for the equation and can be graphed to find specific points like (1, -5).
- The equation t = -4h + 21 reflects the temperature change in Burrtown, starting at 21°F and decreasing by 4°F each hour.
- A linear equation represents relationships between variables, such as cost, temperature, or deposits over time, often indicated in slope-intercept form y = mx + b.
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Test your understanding of slope-intercept equations in this flashcard quiz. Each card focuses on evaluating functions and interpreting graphs in the context of algebra. Perfect for mastering the concepts presented in Chapter 4.2.3.
