Questions and Answers
Is the equation y=2x-1 a linear equation? If so, write it in standard form.
Yes, Ax + By = C form is 2x - y = 1.
What is the y-intercept from the equation 3x - 2y = -6?
(0, 3)
How far does a car travel in 7 hours at a rate of 58 miles per hour?
406 miles
What are the x and y intercepts of the equation 3x - y = 3?
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What is the zero of the equation 3x - 45 = 0?
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What is the slope of the points (5, 8) and (-4, 6)?
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What is the slope of the points (9, 4) and (5, -3)?
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What is the value of r in the points (3, 2) and (r, -4) with m = 3/2?
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Is the function given by the points (0, 1), (-2, -1), and (-4, 1) linear?
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What is the annual rate of change in the number of students in the Delaware High School band from 2004 to 2010?
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Study Notes
Linear Equations
- Equation form: Ax + By = C; confirms the representation of linear equations.
- Example conversion: y = 2x - 1 is a linear equation; standard form representation is 2x - y = 1.
y-Intercept
- Determining the y-intercept from the equation 3x - 2y = -6 leads to finding the point (0, 3).
Distance and Rate
- A car traveling at 58 miles per hour for 7 hours can be estimated to cover 406 miles, derived from the equation d = 58t.
Intercepts
- For the equation 3x - y = 3, the x-intercept is (15, 0) and the y-intercept is (0, -3).
Solving Equations
- Finding the zero of the equation 3x - 45 = 0 results in the root being (15, 0).
Slope Calculation
- The slope between points (5, 8) and (-4, 6) is computed to be 2/9.
- For points (9, 4) and (5, -3), the slope is calculated as 7/4.
Unknown Variable
- Given points (3, 2) and (r, -4) with a slope of 3/2, the value of r is determined to be -1.
Linear Function Test
- A given set of points shows a non-linear relationship, as plotted coordinates (0, 1), (-2, -1), and (-4, 1) do not form a straight line.
Rate of Change
- From 2004 to 2010, the Delaware High School band increased from 275 to 305 students, calculating as an increase of 5 students per year.
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Description
Test your knowledge with these flashcards from Algebra 1 Chapter 3. This mid chapter review covers concepts such as linear equations, y-intercepts, and distance formulas. Perfect for students looking to reinforce their understanding of essential algebraic principles!
