Podcast
Questions and Answers
What is the solution for a in the equation 6a - 15 = 72?
What is the solution for a in the equation 6a - 15 = 72?
14 1/2
The solution x = 73 in the equation 1216 = 12x + 340 gives the number of hours Sheena worked at her job last month.
The solution x = 73 in the equation 1216 = 12x + 340 gives the number of hours Sheena worked at her job last month.
True
How much did Manfred pay per month at the rec center if he paid $193 for one year, including a $25 membership fee?
How much did Manfred pay per month at the rec center if he paid $193 for one year, including a $25 membership fee?
14
The value 8.5 in Bora's savings problem is reasonable and indicates how many months he needs to save for the computer.
The value 8.5 in Bora's savings problem is reasonable and indicates how many months he needs to save for the computer.
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What is the equation of the linear function that models the relationship between x and y in the provided table?
What is the equation of the linear function that models the relationship between x and y in the provided table?
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Hollis's equation y + 13 = (x - 15) is correct for the line passing through the points (15, −13) and (16, −11).
Hollis's equation y + 13 = (x - 15) is correct for the line passing through the points (15, −13) and (16, −11).
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Louetta made a mistake when rewriting -4x - y = 28 in slope-intercept form.
Louetta made a mistake when rewriting -4x - y = 28 in slope-intercept form.
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Which graph correctly represents the linear relationship shown in the table for Jim's guitar lessons?
Which graph correctly represents the linear relationship shown in the table for Jim's guitar lessons?
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Which graph correctly represents the equation y + 3 = -8(x + 2)?
Which graph correctly represents the equation y + 3 = -8(x + 2)?
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Which graph correctly represents the equation y = -53x + 6?
Which graph correctly represents the equation y = -53x + 6?
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Which graph correctly shows the x- and y-intercepts of the line represented by the equation 9x - 5y = 15?
Which graph correctly shows the x- and y-intercepts of the line represented by the equation 9x - 5y = 15?
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What is the y-value of the coordinate for the graph of the equation y = 4x + 2 when x = 1?
What is the y-value of the coordinate for the graph of the equation y = 4x + 2 when x = 1?
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Which of these is a solution to the equation graphed below?
Which of these is a solution to the equation graphed below?
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What is the equation in slope-intercept form for the line represented by the given graph?
What is the equation in slope-intercept form for the line represented by the given graph?
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Which of these identifies key features of the line and the equation in slope-intercept form?
Which of these identifies key features of the line and the equation in slope-intercept form?
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Which equation in point-slope form correctly represents the line in the graph?
Which equation in point-slope form correctly represents the line in the graph?
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Which graph correctly shows the system of equations {y = x - 6, 2x + y = 6}?
Which graph correctly shows the system of equations {y = x - 6, 2x + y = 6}?
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What is the estimated intersection point of the two lines from the system {y = 2x + 2, y = -1/2x - 3}?
What is the estimated intersection point of the two lines from the system {y = 2x + 2, y = -1/2x - 3}?
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After [blank a] minutes, both cars were traveling at a speed of [blank b] miles per hour.
After [blank a] minutes, both cars were traveling at a speed of [blank b] miles per hour.
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The lines of the given system of equations coincide, having an infinite number of solutions.
The lines of the given system of equations coincide, having an infinite number of solutions.
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Study Notes
Solving Linear Equations
- To solve for a in the equation 6a - 15 = 72, the result is 14 1/2.
- In Sheena's case, her earnings equation 1216 = 12x + 340 indicates that x = 73 represents the total hours worked last month.
Membership and Payment Models
- Manfred paid $193 for a one-year membership which includes a $25 one-time fee, leading to a monthly payment of $14.
- Bora's savings plan shows he needs 8.5 months to save enough for a computer priced at $1,105, validating the created equation 1105 = 65m + 552.5.
Linear Functions and Graphs
- A linear function modeled by a specific relationship is expressed as y = 3x - 11.
- The line's equation represented by points (15, -13) and (16, -11) is mistakenly written. The correct form should include the true slope, y + 13 = 2(x - 15).
Slope-Intercept Form and Graph Analysis
- Louetta correctly rewrites the equation -4x - y = 28 into slope-intercept form without errors.
- Graphs for various equations such as y + 3 = -8(x + 2), y = -53x + 6, and the intercepts of 9x − 5y = 15 can be referenced through provided links.
Key Coordinates and Features
- For the equation y = 4x + 2, the y-value at a specific coordinate is 6.
- One solution to a given graphed equation is the point (4, -1).
Slope-Intercept Form and Key Features
- The line's equation from a graph can be represented as y = -5/2x - 2, showing a slope of -5/2.
- Another line has a y-intercept of point (0, -4) and a slope of -2/1, forming the equation y = -2x - 4.
Point-Slope Form Representation
- The equation in point-slope form derived from a graph is y - 0 = -1/3(x + 2).
Systems of Equations
- The system of equations {y = x - 6, 2x + y = 6} can be visualized in a graph.
- The estimated intersection point of the lines defined by {y = 2x + 2, y = -1/2x - 3} is (-2, -2).
Speed of Cars
- After 5 minutes, two cars reach a speed of 45 miles per hour, one increasing and the other decreasing in speed.
- A system of equations graphed results in coinciding lines, indicating an infinite number of solutions.
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Description
Test your understanding of linear equations, membership models, and graph analysis. This quiz covers solving for variables, interpreting functions, and rewriting equations in slope-intercept form. Challenge your knowledge with practical examples and problems.
