Questions and Answers
What is slope-intercept form for the equation of a line?
y=mx+b
The b in y=mx+b is the?
y-intercept (where the line crosses the y-axis)
The m in the y=mx+b is the?
slope of the line (rise over run)
What is the slope formula?
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Give an example of undefined slope.
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Give an example of zero slope.
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Give an example of positive slope.
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Give an example of negative slope.
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Write the equation if b = 3 and m = -2.
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Write the equation if b = -7 and m = 1/2.
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What does the graph of y = -3/2x + 3 look like?
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To write the equation of a line, you need to find what?
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What is the Y-intercept?
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What is the slope of a horizontal line?
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What is the slope of a vertical line?
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What is the y-intercept of a vertical line?
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At what point do you start graphing the line y=x?
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How do you count the slope for the line y=x?
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What is the equation for a horizontal line that goes through 5?
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What is the equation for a vertical line that goes through 5?
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What happens when you subtract a negative?
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What does -3/-6 simplify down to?
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Study Notes
Slope-Intercept Form
- Slope-intercept form is represented by the equation y = mx + b.
- m indicates the slope, calculated as the rise over the run.
- b represents the y-intercept, where the line intersects the y-axis.
Slope Formulas and Characteristics
- Slope formula measures the steepness of a line.
- Undefined slope occurs with vertical lines; there is no defined slope for these lines.
- Zero slope occurs with horizontal lines; these lines maintain a constant y-value.
- Positive slope indicates an upward trend as you move along the x-axis, while negative slope shows a downward trend.
Graphing Lines
- To construct a line’s equation, you must determine the slope (m) and y-intercept (b).
- The y-intercept is the coordinate point where the line intersects the y-axis.
- For the line y = x, begin graphing at the origin (0,0) and move up one unit and right one unit to plot points.
Equations of Specific Lines
- A horizontal line passing through y = 5 is represented as y = 5.
- A vertical line passing through x = 5 is written as x = 5.
Special Cases
- y = -3/2x + 3 generates a line with a negative slope and a y-intercept of 3.
- The equation derived from values b = 3 and m = -2 is y = -2x + 3.
- When b = -7 and m = 1/2, the equation is y = 1/2x - 7.
Simplification and Operations
- Subtracting a negative number equates to adding that number.
- The fraction -3/-6 simplifies to 1/2.
Key Points
- The slope of a horizontal line is always 0.
- A vertical line's slope is deemed undefined.
- A vertical line does not possess a y-intercept at any point.
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Description
Test your knowledge of the slope-intercept form, y=mx+b, with these flashcards designed for Algebra 1. Each card includes key terms such as the slope and y-intercept, along with their definitions. Perfect for reinforcing your understanding of linear equations.
