Podcast
Questions and Answers
What is the solution for the equation $2x + 6 = 0$?
What is the solution for the equation $2x + 6 = 0$?
- -6
- 0
- 3
- -3 (correct)
What is the solution for the equation $3 - x = -9$?
What is the solution for the equation $3 - x = -9$?
- 12
- 9
- -12
- 6 (correct)
What is the solution for the equation $12 + 3x = -6$?
What is the solution for the equation $12 + 3x = -6$?
- 6
- -6
- -4 (correct)
- 0
In linear equations, what does the term 'gradient' refer to?
In linear equations, what does the term 'gradient' refer to?
If the gradient of a line is 2, what does this imply about the line?
If the gradient of a line is 2, what does this imply about the line?
What is the value of $y$ when $x = -2$ in the equation of a line with the equation $y = 3x + 1$?
What is the value of $y$ when $x = -2$ in the equation of a line with the equation $y = 3x + 1$?
For the linear equation in standard form $Ax + By = C$, what does 'C' represent?
For the linear equation in standard form $Ax + By = C$, what does 'C' represent?
What is the $y$-intercept when the linear equation is given as $y = 2x + 5$?
What is the $y$-intercept when the linear equation is given as $y = 2x + 5$?
What is the $y$-intercept of the equation $y = 2x + 5$?
What is the $y$-intercept of the equation $y = 2x + 5$?
How would you label the graph of the equation $4x - 2y = 12$?
How would you label the graph of the equation $4x - 2y = 12$?
If Rudolph's Taxi Service fare is $47.60, how far did the taxi go?
If Rudolph's Taxi Service fare is $47.60, how far did the taxi go?
What is the definition of gradient in a linear graph?
What is the definition of gradient in a linear graph?
In the equation $y = mx + c$, which represents the slope in the cost and time graph for Gustav's fridge repair?
In the equation $y = mx + c$, which represents the slope in the cost and time graph for Gustav's fridge repair?
What does the y-intercept represent in a linear equation?
What does the y-intercept represent in a linear equation?
If the repairman works for 2.5 hours, what would the cost be for Gustav?
If the repairman works for 2.5 hours, what would the cost be for Gustav?
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?
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?
What is the $x$-intercept of the line represented by $y = 2x + 5$?
What is the $x$-intercept of the line represented by $y = 2x + 5$?
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?
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?
In how many minutes would Gustav incur a cost of $100 for the fridge repair?
In how many minutes would Gustav incur a cost of $100 for the fridge repair?
Which equation best represents the relationship between cost (y) and time (x) for Gustav's repair service?
Which equation best represents the relationship between cost (y) and time (x) for Gustav's repair service?
For the set of coordinates (-2, -4), (-1, -8), (0, -12), and (1, -16), what is the y-intercept?
For the set of coordinates (-2, -4), (-1, -8), (0, -12), and (1, -16), what is the y-intercept?
In a linear graph, which of the following represents a consistent gradient?
In a linear graph, which of the following represents a consistent gradient?
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?
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?
What would be the gradient of a horizontal line on a graph?
What would be the gradient of a horizontal line on a graph?
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.
