Questions and Answers
What is the y-intercept?
The point where the graph crosses the y-axis. It has the coordinates (0, y).
What is the x-intercept?
The point where the graph crosses the x-axis. It has the coordinates (x, 0).
What is slope intercept form?
y = mx + b
What is the slope of the line represented by y = x + 9?
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Write the equation of the line whose slope is 5 and y-intercept is (0,-7).
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What is the slope of the line represented by y = 5x - 7?
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Write the equation of the line that passes through (0,-6) and (4,10).
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Write the point-slope equation of the line that passes through (7, 3) whose slope is 2.
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What is the x-intercept of the line 5x - 2y = 10?
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Study Notes
Key Concepts in Algebra 1
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Y-Intercept
- Defined as the point where the graph intersects the y-axis, represented as (0, y).
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X-Intercept
- Defined as the point where the graph intersects the x-axis, represented as (x, 0).
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Slope-Intercept Form
- The general equation for linear functions, expressed as ( y = mx + b ) where:
- ( m ) is the slope
- ( b ) is the y-intercept
- The general equation for linear functions, expressed as ( y = mx + b ) where:
Slope of Lines
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For the equation ( y = x + 9 ):
- The slope is represented as ( 1 ) (or ( 1x )).
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For the equation ( y = 5x - 7 ):
- The slope is ( 5 ).
Writing Equations of Lines
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When given a slope of ( 5 ) and a y-intercept of (0, -7):
- The equation is formulated as ( y = 5x - 7 ).
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For a line passing through the points (0, -6) and (4, 10):
- The equation determined is ( y = 4x - 6 ).
Point-Slope Form
- To write the equation of a line using point-slope form passing through (7, 3) with a slope of ( 2 ):
- The equation is ( y - 3 = 2(x - 7) ).
Intercepts of a Line
- For the line represented by ( 5x - 2y = 10 ):
- The x-intercept is (2, 0), and the y-intercept is (0, -5).
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Description
This quiz covers fundamental concepts in Algebra 1, including Y-Intercept, X-Intercept, and the Slope-Intercept Form. Additionally, it explores how to determine slopes from equations and write equations for lines based on given points and slopes. Test your understanding of these key algebraic principles.
