Lesson 2 of 4
Use points, slope and intercepts to describe a straight graph.
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Big ideas · 1 of 8
Big ideas
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For distinct inputs x1 and x2, SlopeVertical change divided by horizontal change.Exactly: For a nonvertical line through distinct points and , its slope is .Mix-up alert: A vertical line has undefined slope; a horizontal line has slope zero.See this in Key words is . Use the same point order in numerator and denominator.
Slope-intercept form is . Point-slope form uses a known point directly. Both can describe the same nonvertical line.
A described graph with two points, or a slope and one point, gives enough information for a unique nonvertical line. Verify the resulting rule at both stated points.
Horizontal lines have slope zero; vertical lines have undefined slope. Distinct nonvertical parallel lines have equal slopes. For two nonvertical perpendicular lines, the slopes multiply to -1; horizontal and vertical lines are also perpendicular.
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Worked example: two points to a rule
Whole picture, 4 steps
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Wrong idea: slope is change in x divided by change in y. Slope in y versus x is output change over input change. Label the two changes before forming the ratio.
Worked example
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Worked example
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Expanding gives .
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Flashcards
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Card 1 of 8
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Output change 6 divided by input change 2.
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What is the slope between and ?
3.
What is point-slope form?
.
What is the y-intercept of ?
.
What is the x-intercept of ?
.
What slope does a horizontal line have?
0.
What slope does a vertical line have?
Undefined.
How are slopes of nonvertical parallel lines related?
They are equal.
How are slopes of perpendicular nonvertical lines related?
Their product is −1.
True or false
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Self-test
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6 questions. One at a time.
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Self-test
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6 questions. One at a time.
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Write it
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Match
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Connect the ideas
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Homework · 3 points
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Homework
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https://gradebridge-beryl.vercel.app/learn/precalculus/linear-functions/line-equations#homework
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