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Questions and Answers
What is the solution for the equation $2x + 6 = 0$?
What is the solution for the equation $3 - x = -9$?
What is the solution for the equation $12 + 3x = -6$?
In linear equations, what does the term 'gradient' refer to?
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If the gradient of a line is 2, what does this imply about the line?
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What is the value of $y$ when $x = -2$ in the equation of a line with the equation $y = 3x + 1$?
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For the linear equation in standard form $Ax + By = C$, what does 'C' represent?
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What is the $y$-intercept when the linear equation is given as $y = 2x + 5$?
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What is the $y$-intercept of the equation $y = 2x + 5$?
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How would you label the graph of the equation $4x - 2y = 12$?
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If Rudolph's Taxi Service fare is $47.60, how far did the taxi go?
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What is the definition of gradient in a linear graph?
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In the equation $y = mx + c$, which represents the slope in the cost and time graph for Gustav's fridge repair?
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What does the y-intercept represent in a linear equation?
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If the repairman works for 2.5 hours, what would the cost be for Gustav?
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If a table shows the values of x from -2 to 0 and the corresponding values of y are 0, 1, 2, 3, what is the gradient?
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What is the $x$-intercept of the line represented by $y = 2x + 5$?
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Given a linear table with x values of -2, -1, 0 and corresponding y values of -4, -8, -12, what is the gradient of the line?
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In how many minutes would Gustav incur a cost of $100 for the fridge repair?
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Which equation best represents the relationship between cost (y) and time (x) for Gustav's repair service?
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For the set of coordinates (-2, -4), (-1, -8), (0, -12), and (1, -16), what is the y-intercept?
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In a linear graph, which of the following represents a consistent gradient?
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If a linear graph has a gradient of 3, which of the following could be true for two points (x1, y1) and (x2, y2) on the line?
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What would be the gradient of a horizontal line on a graph?
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Study Notes
Gradient and y-intercept
- Gradient is the measure of steepness of a line.
- The gradient is represented by the letter m.
- Gradient is calculated using the formula: m = (change in y) / (change in x).
- The y-intercept is the point where the line crosses the y-axis.
- The y-intercept is represented by the letter c.
Linear relationships
- Positive gradient: The line slopes upwards from left to right.
- Negative gradient: The line slopes downwards from left to right.
- Zero gradient: The line is horizontal.
- Undefined gradient: The line is vertical.
Finding the gradient and y-intercept from a table
- Gradient is found by calculating the difference in y values divided by the difference in x values for any two points on the line.
- Y-intercept is found by identifying the y value when x is equal to zero.
Equation of a line
- The equation of a line is in the form y = mx + c, where m is the gradient and c is the y-intercept.
- x-intercept is found by setting y to zero and solving for x in the equation.
- y-intercept is found by setting x to zero and solving for y in the equation.
Linear relationships in real-world scenarios
- Taxi fare - the cost is a linear function of the distance travelled.
- Repair costs - the cost is a linear function of the time taken.
- Cost of goods - the cost is a linear function of the quantity purchased.
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Description
Test your understanding of gradients and y-intercepts in linear equations. This quiz covers concepts like positive, negative, zero, and undefined gradients, as well as how to calculate them from tables and identify y-intercepts. Perfect for students studying algebra.
