What does the constant represent in the equation of a straight line ?
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What does the constant represent in the equation of a straight line ?
In the equation of a straight line , the constant represents the gradient of the line.
True or False?
In the equation of a line , the constant tells you where the line crosses the x-axis.
False.
In the equation of a line , the constant 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 in the equation of a line refers to the y-intercept.
False.
The constant in the equation of a line does not refer to the y-intercept.
You need to rearrange it to make 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 where is the gradient
Substitute the coordinates of the point into the equation for and
Solve the equation to find
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 .
Find the gradient, , using the coordinates (e.g. form a right-angled triangle)
Substitute one pair of coordinates into to find
True or False?
The gradient of the line with the equation is 2.
False.
The gradient of the line with the equation is not 2. You need to write it in the form first, giving . Therefore the gradient is -2.
How do you sketch the line ?
To sketch the line :
Substitute to find where it crosses the y-axis
Substitute 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 ?
To sketch the line :
plot the point
find another point by substituting in another value for
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 .
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 and are parallel.
False.
The lines and 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:
is equal to the gradient of the parallel line
substitute the coordinates of the point into and solve to find
What is the gradient of a line that is parallel to the line ?
The gradient of a line that is parallel to the line is .
Define perpendicular lines.
Two perpendicular lines intersect at right angles (90°).
The lines and are perpendicular. State the relationship between and .
If the lines and are perpendicular, then .
This can be written as or .
The gradients are negative reciprocals of one another.
True or False?
The lines and are perpendicular.
False.
The lines and are not perpendicular.
This is because not .
and would be perpendicular.
What is the gradient of a line that is perpendicular to the line ?
The gradient of a line that is perpendicular to the line is .
True or False?
The line is perpendicular to the line .
True.
The line is perpendicular to the line . The first line is horizontal and the second is vertical.