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Questions and Answers
Which graph could represent the leaf's height in feet as a function of time, in seconds, after leaving the branch?
Which graph could represent the leaf's height in feet as a function of time, in seconds, after leaving the branch?
- Graph C
- Graph B
- Graph D (correct)
- Graph A
What are the slope and y-intercept of the linear function graphed?
What are the slope and y-intercept of the linear function graphed?
slope: b; y-intercept: 1
Which statements are true about the lines forming trapezoid WXYZ? Select three options.
Which statements are true about the lines forming trapezoid WXYZ? Select three options.
- Line XW has a greater slope than line YZ
- Line ZW has the same y-intercept as line YZ (correct)
- Line XW has a lesser slope than line YZ (correct)
- Line WZ has the same slope as line XY (correct)
What is the y-intercept of the function f(x) = -x + ?
What is the y-intercept of the function f(x) = -x + ?
Which graph represents a line with a slope of _ and a y-intercept equal to that of the line y = x - 2?
Which graph represents a line with a slope of _ and a y-intercept equal to that of the line y = x - 2?
Which equation represents Grant's path in the pool?
Which equation represents Grant's path in the pool?
Which equation represents Nolan's line?
Which equation represents Nolan's line?
What is the slope of the line represented by the equation y = -5/3 - 5x?
What is the slope of the line represented by the equation y = -5/3 - 5x?
Which equation can be used to determine m, the number of measures Harita still needs to memorize?
Which equation can be used to determine m, the number of measures Harita still needs to memorize?
Which equation represents y, the profit earned by the hot dog stand for x hot dogs sold?
Which equation represents y, the profit earned by the hot dog stand for x hot dogs sold?
What equation represents the graphed function?
What equation represents the graphed function?
Which equation represents the revenue in dollars as a function of greeting cards sold?
Which equation represents the revenue in dollars as a function of greeting cards sold?
What is the slope of the line represented by the equation y = 4/5x - 3?
What is the slope of the line represented by the equation y = 4/5x - 3?
What is the slope of the line represented by the equation y = -1/2x + 1/4?
What is the slope of the line represented by the equation y = -1/2x + 1/4?
What is the y-intercept of the function f(x) = -2/9x + 1/3?
What is the y-intercept of the function f(x) = -2/9x + 1/3?
Which equation represents Nolan's line?
Which equation represents Nolan's line?
Flashcards
What is slope-intercept form?
What is slope-intercept form?
The standard form of a linear equation representing a straight line where 'm' is the slope (rise over run) and 'b' is the y-intercept (where the line crosses the y-axis).
What is slope?
What is slope?
The rate of change of a line, representing how much the y-value changes for every unit change in the x-value.
What is y-intercept?
What is y-intercept?
The point where a line intersects the y-axis, represented by the value of 'b' in the slope-intercept form (y = mx + b).
Why is slope-intercept form useful?
Why is slope-intercept form useful?
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What is the slope-intercept form equation?
What is the slope-intercept form equation?
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What is the slope of the line represented by the equation y = 2x + 3?
What is the slope of the line represented by the equation y = 2x + 3?
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What is the y-intercept of the line represented by the equation y = 2x + 3?
What is the y-intercept of the line represented by the equation y = 2x + 3?
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What is the slope of the line represented by the equation y = -5x - 2/3?
What is the slope of the line represented by the equation y = -5x - 2/3?
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What is the y-intercept of the line represented by the equation y = -5x - 2/3?
What is the y-intercept of the line represented by the equation y = -5x - 2/3?
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What is the slope of the line represented by the equation y = 4/5x - 3?
What is the slope of the line represented by the equation y = 4/5x - 3?
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What is the y-intercept of the line represented by the equation y = 4/5x - 3?
What is the y-intercept of the line represented by the equation y = 4/5x - 3?
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What is the slope of the line represented by the equation y = -1/2x + 1/4?
What is the slope of the line represented by the equation y = -1/2x + 1/4?
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What is the y-intercept of the line represented by the equation y = -1/2x + 1/4?
What is the y-intercept of the line represented by the equation y = -1/2x + 1/4?
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What is the y-intercept of the function f(x) = -2/9x + 1/3?
What is the y-intercept of the function f(x) = -2/9x + 1/3?
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What is the slope of the line defined by the equation y = -1/3x + 3?
What is the slope of the line defined by the equation y = -1/3x + 3?
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What is the y-intercept of the line defined by the equation y = -1/3x + 3?
What is the y-intercept of the line defined by the equation y = -1/3x + 3?
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What is the slope of the line represented by the equation m = 90 - 6d?
What is the slope of the line represented by the equation m = 90 - 6d?
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What is the y-intercept of the line represented by the equation m = 90 - 6d?
What is the y-intercept of the line represented by the equation m = 90 - 6d?
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Study Notes
Slope-Intercept Form of a Line
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Slope-intercept form of a line is represented as ( y = mx + b ) where ( m ) is the slope and ( b ) is the y-intercept.
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A leaf falls from a height of 12 feet at a rate of 0.25 feet/sec. Its height as a function of time can be modeled using linear equations.
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For a graphed linear function, the slope is given as an upward or downward trajectory while the y-intercept corresponds to the point where the line intersects the y-axis.
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In trapezoid WXYZ formed by lines on a coordinate plane:
- Line WZ has the same slope as line XY.
- Line XW has a lesser slope compared to line YZ.
- Line ZW shares the same y-intercept as line YZ.
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For the function ( f(x) = -x + ? ), the y-intercept is calculated to be ( \frac{1}{3} ).
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To determine a line with a specific slope and y-intercept that corresponds to ( y = x - 2 ), analyze graphs to identify these characteristics.
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Grant’s swimming path in a pool modeled on a coordinate graph can be defined with the equation ( y = 4 - \frac{x}{2} ).
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Nolan plots a line with a y-intercept of (0, 3) and a slope of 2, leading to the equation ( y = 2x + 3 ).
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The line represented by the equation ( y = -\frac{2}{3} - 5x ) has a slope of -5.
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For Harita's music measures, her process of memorizing measures yields the equation ( m = 90 - 6d ).
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The profit function for a hot dog stand is dependent on sales. The equation ( y = 2x - 48 ) captures the profit based on ( x ) hot dogs sold.
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A linear equation representing a graphed function could be ( y = -\frac{1}{3}x + 3 ).
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Revenue generated by greeting cards sold is modeled by ( y = 4x ), indicating the profit earned per card.
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The slope of the equation ( y = \frac{4}{5} x - 3 ) is ( \frac{4}{5} ).
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For the equation ( y = -\frac{1}{2}x + \frac{1}{4} ), the slope is calculated to be -0.5.
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The y-intercept of the function ( f(x) = -\frac{2}{9}x + \frac{1}{3} ) is found to be ( \frac{1}{3} ).
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Nolan’s plotted line with a y-intercept of (0, 3) and a slope of 2 is again defined by the equation ( y = 2x + 3 ).
Studying That Suits You
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Description
Test your understanding of the slope-intercept form of a line with this quiz. Each flashcard presents scenarios and questions that challenge your knowledge of linear functions. Perfect for students learning algebra concepts.
