True or False? On a coordinate grid, the point which is 3 units right and 4 units up from the origin has coordinates (3,4) .

True. On a coordinate grid, the point which is 3 units right and 4 units up from the origin has coordinates (3,4) .

What does the gradient of a line measure?

The gradient of a line measures the steepness of the line.

True or False? A line with a gradient of -4 is steeper than a line with a gradient of -5 .

False. A line with a gradient of -5 is steeper than a line with a gradient of -4 . The steeper line is the one with the bigger gradient value when you ignore negative signs.

True or False? A positive gradient means the line goes upwards from bottom left to top right .

True. A positive gradient means the line goes upwards from bottom left to top right .

What two bits of information do you need to find the equation of a straight line ?

To find the equation of a straight line you need: the gradient of the line a point on the line (it could be the y-intercept)

Define the term y -intercept .

The y -intercept is where a graph crosses the y -axis .

If two lines are parallel then what is the relationship between the gradients of the lines?

If two lines are parallel then their gradients are equal .

IGCSEMathsCambridge (CIE)CoreFlashcardsCoordinate Geometry & GraphsLinear Graphs

Linear Graphs (Cambridge (CIE) IGCSE Maths: Core): Flashcards

Exam code: 0580 & 0980

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True or False?
On a coordinate grid, the point which is 3 units right and 4 units up from the origin has coordinates (3,4).

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Cards in this collection (20)

True or False?
On a coordinate grid, the point which is 3 units right and 4 units up from the origin has coordinates (3,4).
True.
On a coordinate grid, the point which is 3 units right and 4 units up from the origin has coordinates (3,4).
Which coordinates would be $a$ units left and $b$ units down from the point $(x, y)$ ?
The coordinates $a$ units left and $b$ units down from the point $(x, y)$ would be $(x - a, y - b)$ .
What does the gradient of a line measure?
The gradient of a line measures the steepness of the line.
True or False?
A line with a gradient of -4 is steeper than a line with a gradient of -5.
False.
A line with a gradient of -5 is steeper than a line with a gradient of -4. The steeper line is the one with the bigger gradient value when you ignore negative signs.
True or False?
The gradient of a line is equal to $\frac{change in y}{change in x}$ .
True.
The gradient of a line is equal to $\frac{change in y}{change in x}$ .
State the formula for the gradient of the line that passes through $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ .
The formula for the gradient of the line that passes through $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ is $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .
The formula $m = \frac{y_{1} - y_{2}}{x_{1} - x_{2}}$ will also give the gradient.
True or False?
A positive gradient means the line goes upwards from bottom left to top right.
True.
A positive gradient means the line goes upwards from bottom left to top right.
True or False?
The gradient of the line which passes through $(4, 5)$ and $(1, 2)$ can be found by calculating $\frac{2 - 5}{4 - 1}$ .
False.
The gradient of the line which passes through $(4, 5)$ and $(1, 2)$ can not be found by calculating $\frac{2 - 5}{4 - 1}$ .
The order needs to be consistent. If the second coordinate is used first for the $y$ coordinates, then the second coordinate should be used first for the $x$ coordinates.
It should be either $\frac{2 - 5}{1 - 4}$ or $\frac{5 - 2}{4 - 1}$ .
What does the constant $m$ represent in the equation of a straight line $y = m x + c$ ?
In the equation of a straight line $y = m x + c$ , the constant $m$ represents the gradient of the line.
True or False?
In the equation of a line $y = m x + c$ , the constant $c$ tells you where the line crosses the x-axis.
False.
In the equation of a line $y = m x + c$ , the constant $c$ tells you where the line crosses the y-axis.
What two bits of information do you need to find the equation of a straight line?
To find the equation of a straight line you need:
- the gradient of the line
- a point on the line (it could be the y-intercept)
Define the term y-intercept.
The y-intercept is where a graph crosses the y-axis.
True or False?
The constant $c$ in the equation of a line $a x + b y + c = 0$ refers to the y-intercept.
False.
The constant $c$ in the equation of a line $a x + b y + c = 0$ does not refer to the y-intercept.
You need to rearrange it to make $y$ the subject.
How do you find the equation of a line if you know the gradient and a point on the line?
If you know the gradient of a line and a point on the line, then to find the equation:
- write $y = m x + c$ where $m$ is the gradient
- Substitute the coordinates of the point into the equation for $x$ and $y$
- Solve the equation to find $c$
How can you find the equation of a straight line if you have the coordinates of two points on the line?
If you have the coordinates of two points on a straight line then you can find the equation of the line $y = m x + c$ .
1. Find the gradient, $m$ , using the coordinates (e.g. form a right-angled triangle)
2. Substitute one pair of coordinates into $y = m x + c$ to find $c$
True or False?
The gradient of the line with the equation $2 x + y + 5 = 0$ is 2.
False.
The gradient of the line with the equation $2 x + y + 5 = 0$ is not 2. You need to write it in the form $y = m x + c$ first, giving $y = - 2 x - 5$ . Therefore the gradient is -2.
If two lines are parallel then what is the relationship between the gradients of the lines?
If two lines are parallel then their gradients are equal.
True or False?
The lines $y = 4 x + 5$ and $y = 3 x + 5$ are parallel.
False.
The lines $y = 4 x + 5$ and $y = 3 x + 5$ are not parallel because the gradients are different. They both have the same y-intercept.
How do you find the equation of a line if you know a point on the line and you know the equation of a line it is parallel to?
If you know a point on a line and you know the equation of a line it is parallel to then you can find the equation of the line:
- $m$ is equal to the gradient of the parallel line
- substitute the coordinates of the point into $y = m x + c$ and solve to find $c$
What is the gradient of a line that is parallel to the line $y = 3 x - 2$ ?
The gradient of a line that is parallel to the line $y = 3 x - 2$ is $3$ .

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