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What does 'm' represent in the slope-intercept form of a line?
What does 'm' represent in the slope-intercept form of a line?
In the equation y = mx + b, 'b' is the x-intercept.
In the equation y = mx + b, 'b' is the x-intercept.
False
What is the general form of a linear equation in slope-intercept form?
What is the general form of a linear equation in slope-intercept form?
y = mx + b
The point where the line crosses the y-axis is known as the ______.
The point where the line crosses the y-axis is known as the ______.
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Match the following components of the slope-intercept form with their definitions:
Match the following components of the slope-intercept form with their definitions:
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Which of the following equations is in slope-intercept form?
Which of the following equations is in slope-intercept form?
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The slope of a line can be determined directly from its graph.
The slope of a line can be determined directly from its graph.
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What is the slope of the equation $y = -\frac{1}{2}x + 2$?
What is the slope of the equation $y = -\frac{1}{2}x + 2$?
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The y-intercept of the equation $y = 3x + 5$ is 5.
The y-intercept of the equation $y = 3x + 5$ is 5.
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What is the value of the y-intercept (b) when given the equation $y = -4x + 7$?
What is the value of the y-intercept (b) when given the equation $y = -4x + 7$?
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In the equation $y = mx + b$, the letter 'm' stands for the ______.
In the equation $y = mx + b$, the letter 'm' stands for the ______.
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Match the following components of the linear equation with their definitions:
Match the following components of the linear equation with their definitions:
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What is the equation of the line with a slope of 1 and a y-intercept of -3?
What is the equation of the line with a slope of 1 and a y-intercept of -3?
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The slope of a horizontal line is 0.
The slope of a horizontal line is 0.
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If the slope of a line is negative, what does this indicate about the direction of the line?
If the slope of a line is negative, what does this indicate about the direction of the line?
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The equation of the line in slope-intercept form is written as $y = mx + ______$.
The equation of the line in slope-intercept form is written as $y = mx + ______$.
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The y-intercept of the function given as $y = 500x + 100$ is 500.
The y-intercept of the function given as $y = 500x + 100$ is 500.
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What is the y-value when x = 1 for the equation $y = 500x + 100$?
What is the y-value when x = 1 for the equation $y = 500x + 100$?
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In the equation $y = mx + b$, the value of m represents the _____ of the line.
In the equation $y = mx + b$, the value of m represents the _____ of the line.
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Match the following terms with their definitions:
Match the following terms with their definitions:
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Which of the following equations represents a line with a negative slope?
Which of the following equations represents a line with a negative slope?
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The slope of the equation $y = -\frac{1}{2}x - 3$ is positive.
The slope of the equation $y = -\frac{1}{2}x - 3$ is positive.
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Identify the value of b in the equation $y = -\frac{1}{2}x - 3$.
Identify the value of b in the equation $y = -\frac{1}{2}x - 3$.
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The equation for a line in slope-intercept form is written as y = _____ + b.
The equation for a line in slope-intercept form is written as y = _____ + b.
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Study Notes
Linear Equations: y = mx + b
- The equation y = mx + b is the slope-intercept form of a linear equation.
- 'm' represents the slope of the line.
- 'b' represents the y-intercept (the point where the line crosses the y-axis).
- The slope indicates the rate of change of y with respect to x.
- The y-intercept gives the starting value of y when x is zero.
- To graph a line from an equation in the form y = mx + b, plot the y-intercept (0, b) first. Then use the slope (m) to find other points on the line.
- The slope is calculated as the change in y divided by the change in x.
- A nonproportional relationship is represented by a linear equation in the form y=mx+b.
- To write an equation for a given graph of a line, identify the y-intercept and the slope.
Slope-Intercept Form
- A nonproportional relationship is a linear relationship where the graph is not a straight line through the origin (0, 0).
- The slope-intercept form of a linear equation is y = mx + b.
- In this form, 'm' represents the slope and 'b' represents the y-intercept.
- The y-intercept is the point where the line intersects the y-axis.
- The y-coordinate of the y-intercept is 'b'.
Key Concepts
- Finding an equation of a line involves determining the slope and the y-intercept.
- The slope formula is: (y₂ - y₁)/(x₂ - x₁).
- Using the slope and the y-intercept, the equation can be written in the form y = mx + b.
- A graph that shows a relationship should follow a consistent pattern of change.
Example Applications
- Real-world situations involving linear relationships and cost calculations can be represented by linear equations to model trends and determine the total cost.
- Analyzing the cost of rental expenses (Kayak rentals), where a fixed cost is added to the hourly rate, can demonstrate the application of linear relations.
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Description
Explore the slope-intercept form of linear equations, y = mx + b. Understand how to identify the slope and y-intercept, graph the equation, and recognize nonproportional relationships. This quiz will help solidify your grasp of the basic concepts in linear equations.
