Questions and Answers
On a graph of an equation, an ordered pair that is a solution will be _____
on the line
The graph of the equation x=5 will be ____.
vertical
An example of an equation of a horizontal line is:
y=2
An intercept is a point where a line _________.
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To find the y-intercept,___________.
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The formula for slope is m = ______.
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Slope is defined as _____.
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A horizontal line has a _____ slope.
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An example of an undefined slope is _____.
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_______ is a method to write a function showing the input & output.
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Vertical line test is a method to determine if a graph is a _____.
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In f(3) = -5, the input is __.
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The equation for slope-intercept form is ______.
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The letter 'b' in slope-intercept form represents _______.
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When finding the y-intercept, use the given slope & the ______.
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Parallel lines have ______.
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The equation for finding slope is _____.
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To rewrite an equation from point slope form to slope-intercept form, ______.
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The equation for point slope form is _____.
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Absolute value equations or inequalities will have ___ solution.
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You must get the __________ alone before making one answer positive and the other answer negative.
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When you write the 2nd problem in an absolute value with an inequality (the negative answer), you must _________.
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When sketch the of an inequality, < and > means that you have a ___ line.
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After drawing a line of the inequality, use a ________ to find the solutions.
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The shaded part of an inequality graph represents all the ______.
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The line of an inequality separates the coordinate planes into _____.
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Perpendicular lines have _____.
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An equation of a line perpendicular to y=-3x + 4 is ______.
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The letter that represents the y-intercept is ____.
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The equation for a line that has a slope of -1 and a y-intercept of 0 is _____.
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When graphing an equation in slope-intercept form, plot the ______ first.
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In the equation, y=-x, the slope is ____.
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X-1 < 3 ___ x-1 > -3.
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X-1 > -3 ___ x-1 < -3.
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X+5 > 6 ___ x+5 < -6.
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X=7=3 ___ x+7=-3.
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Study Notes
Graphing and Equations
- An ordered pair that satisfies an equation lies on the line of the graph.
- The vertical line represented by the equation x=5 is straight up and down.
- A horizontal line has a constant y value, such as y=2.
Intercepts and Slope
- An intercept is the point where a graph crosses an axis (x-axis or y-axis).
- To locate the y-intercept, substitute 0 for x and solve for y.
Slope Calculations
- The formula for calculating slope (m) is m = (y2 - y1) / (x2 - x1).
- Slope can be defined as the rise over run between two points on a graph.
- A horizontal line has a slope of zero.
Undefined and Defined Slopes
- An example of an undefined slope is when x equals a constant, such as m=-5, 0.
Function and Notation
- Function notation is used to represent output values based on input values, such as in f(x).
- The vertical line test helps determine if a graph represents a function.
Inputs and Equation Forms
- In the function f(3) = -5, the value 3 is the input.
- The slope-intercept form of a line is given by the equation y = mx + b.
- In this equation, b denotes the y-intercept.
Parallel and Perpendicular Lines
- Parallel lines share the same slope but have different y-intercepts.
- Perpendicular lines possess opposite reciprocal slopes.
Characteristics of Lines
- An equation of a line perpendicular to y = -3x + 4 can be expressed as y = 1/3x - 2.
- The y-intercept is indicated by the letter b in the equation.
Special Cases in Equations
- The line described by y = -x has a slope of -1 and a y-intercept at 0.
- When plotting a graph in slope-intercept form, always plot the y-intercept first.
Inequalities and Absolute Value
- Absolute value equations may yield two solutions and require isolating the absolute value expression first.
- In writing the second equation from an absolute value inequality, one must flip the sign.
- A solid line is used to represent inequalities involving < and >, while a dashed line indicates strict inequalities.
Graphing Inequalities
- To find solutions on a graph, utilize a test point after drawing the line.
- The shaded area of an inequality represents all possible solutions.
Domains and Ranges
- The line of an inequality divides the coordinate plane into half-planes.
Compound Inequalities
- Compound inequalities can be represented using and or or statements to combine conditions.
- For example, x - 1 < 3 and x - 1 > -3 forms a compound condition.
Conclusion
- The summary encapsulates key concepts related to graphing, slope, functions, and inequalities in algebra, aiding in understanding essential Algebra 1 topics for final assessments.
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Description
Test your knowledge of Algebra 1 concepts with these multiple choice questions. This quiz covers essential topics such as graphing equations, slopes, and intercepts, perfect for final exam preparation. Review key definitions and terminology to succeed in your studies.
