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 .

What does a line with a negative gradient look like?

A line with a negative gradient will start at the top left and go down to the bottom right.

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 .

Define perpendicular lines.

Two perpendicular lines intersect at right angles (90°).

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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 (20)

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 sketch the line $a x + b y = c$ ?
To sketch the line $a x + b y = c$ :
- Substitute $x = 0$ to find where it crosses the y-axis
- Substitute $y = 0$ to find where it crosses the x-axis
- Draw a line going through the two intercepts
You could also find any other two points on the line and use those.
How do you sketch the line $y = m x + c$ ?
To sketch the line $y = m x + c$ :
- plot the point $(0, c)$
- find another point by substituting in another value for $x$
- plot that point and draw a straight line going through both points
You can also use the gradient; for every one unit to the right, go up/down by $m$ .
What does a line with a negative gradient look like?
A line with a negative gradient will start at the top left and go down to the bottom right.
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 $3$ .
Define perpendicular lines.
Two perpendicular lines intersect at right angles (90°).
The lines $y = m x + c$ and $y = M x + C$ are perpendicular. State the relationship between $m$ and $M$ .
If the lines $y = m x + c$ and $y = M x + C$ are perpendicular, then $m \times M = - 1$ .
This can be written as $m = - \frac{1}{M}$ or $M = - \frac{1}{m}$ .
The gradients are negative reciprocals of one another.
True or False?
The lines $y = 2 x + 3$ and $y = \frac{1}{2} x + 1$ are perpendicular.
False.
The lines $y = 2 x + 3$ and $y = \frac{1}{2} x + 1$ are not perpendicular.
This is because $2 \times \frac{1}{2} = 1$ not $- 1$ .
$y = 2 x + 3$ and $y = - \frac{1}{2} x + 1$ would be perpendicular.
What is the gradient of a line that is perpendicular to the line $y = 3 x - 2$ ?
The gradient of a line that is perpendicular to the line $y = 3 x - 2$ is $- \frac{1}{3}$ .
True or False?
The line $y = 5$ is perpendicular to the line $x = 4$ .
True.
The line $y = 5$ is perpendicular to the line $x = 4$ . The first line is horizontal and the second is vertical.

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