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? When you step out a gradient on a graph, one unit is always one square.

False. The two axes can use different scales , so one square might be worth 2 units, 5 units or half a unit. Read the numbers on each axis before counting any squares.

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 .

GCSEMathsEdexcelFoundationFlashcardsAlgebraLinear Graphs

Linear Graphs (Edexcel GCSE Maths: Foundation): Flashcards

Exam code: 1MA1

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FrontEquations of Straight Lines (y = mx + c)
What does the constant $m$ represent in the equation of a straight line $y = m x + c$ ?
FrontEquations of Straight Lines (y = mx + c)
What two bits of information do you need to find the equation of a straight line?
BackEquations of Straight Lines (y = mx + c)
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)

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Cards in this collection (17)

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.
How do you draw the line $y = 2 x + 1$ without making a table of values?
Start at the $y$ -intercept, the point $(0, 1)$ , then move 1 unit right and 2 units up to reach the next point.
Repeat that step to get more points, then join them with a ruler.
Complete the rule for stepping out a fractional gradient:
A gradient of $\frac{a}{b}$ means $______$ units up for every $______$ units to the right.
The completed rule is:
A gradient of $\frac{a}{b}$ means $a$ units up for every $b$ units to the right.
If the gradient is negative you go down instead of up, so $- \frac{3}{5}$ means 3 units down for every 5 units right.
You are asked to draw $y = 3 x - 1$ on axes running from $x = 0$ to $x = 10$ . Which $x$ values should you choose for your table?
Choose values spread out across the axes given, such as $x = 0$ , $x = 5$ and $x = 10$ .
Points bunched close together make the direction of the line much harder to judge when you come to draw it.
True or False?
When you step out a gradient on a graph, one unit is always one square.
False.
The two axes can use different scales, so one square might be worth 2 units, 5 units or half a unit.
Read the numbers on each axis before counting any squares.
You are given a table of values for a straight-line graph but no equation. How do you draw the graph?
Pair each $x$ value with its $y$ value to form the coordinates $(x, y)$ , and plot those points.
Then draw a straight line through them with a ruler; every point should lie on the line.
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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