Podcast
Questions and Answers
What is the slope of a line that rises from left to right?
What is the slope of a line that rises from left to right?
- Negative
- Undefined
- Zero
- Positive (correct)
A horizontal line has a positive slope.
A horizontal line has a positive slope.
False (B)
What is the formula for finding the slope given two points, (x₁, y₁) and (x₂, y₂)?
What is the formula for finding the slope given two points, (x₁, y₁) and (x₂, y₂)?
m = (y₂ - y₁) / (x₂ - x₁)
In the slope-intercept form, y = mx + b, 'b' represents the ______.
In the slope-intercept form, y = mx + b, 'b' represents the ______.
Match the forms of linear equations with their definitions:
Match the forms of linear equations with their definitions:
To solve the equation 3x + 5 = 20, what is the first step?
To solve the equation 3x + 5 = 20, what is the first step?
In a linear equation, the highest power of the variable is 2.
In a linear equation, the highest power of the variable is 2.
What do you call a line that has an undefined slope?
What do you call a line that has an undefined slope?
If a line passes through points (2, 3) and (4, 7), the slope is ______.
If a line passes through points (2, 3) and (4, 7), the slope is ______.
Which form should be used to write an equation if you have the slope and a point?
Which form should be used to write an equation if you have the slope and a point?
Flashcards
Line
Line
A straight path that extends infinitely in both directions.
Rate of change
Rate of change
The amount a quantity changes over time or in relation to another quantity.
Linear relationship
Linear relationship
A relationship where the rate of change is constant, meaning the line representing it is straight.
Slope
Slope
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Positive slope
Positive slope
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Negative slope
Negative slope
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Zero slope
Zero slope
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Undefined slope
Undefined slope
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Slope-intercept form
Slope-intercept form
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Point-slope form
Point-slope form
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Study Notes
Lines and Linear Relationships
- Lines are straight paths that extend indefinitely in both directions.
- Rate of change describes how much a quantity changes over time or relative to another quantity. In a linear relationship, the rate of change is constant.
- Slope measures the steepness of a line. It is calculated as the vertical change (rise) divided by the horizontal change (run).
- Positive slope: line rises from left to right.
- Negative slope: line falls from left to right.
- Zero slope: horizontal line.
- Undefined slope: vertical line.
Creating and Solving Linear Relations
- A linear relation can be expressed in various forms, including:
- Slope-intercept form: y = mx + b, where 'm' is the slope and 'b' is the y-intercept (the point where the line crosses the y-axis).
- Point-slope form: y - y₁ = m(x - x₁), where 'm' is the slope and (x₁, y₁) is a point on the line.
Finding the Equation of a Line
- From the slope and a point: Use the point-slope form.
- From two points: Use the slope formula first, then the point-slope form.
Solving Linear Equations
- Linear equations involve variables to the first power.
- To solve, isolate the variable using inverse operations.
- Example methods include:
- Combining like terms
- Using the distributive property
- Adding or subtracting to both sides of the equation
- Multiplying or dividing to both sides of the equation
Creating Linear Equations
- Given specific conditions, like slope and a point or two points, use the appropriate forms of the linear equation to derive the equation for the line.
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