Parallel lines
Parallel lines make equal corresponding angles(θ) with the xaxis. Therefore their gradients are equal.
Perpendicular lines
If two lines are perpendicular to eachother, the product of their gradients is 1.
If the gradient of AB is m_{1} and the gradient of CD is m_{2} , then:
Equation of a straight line y = mx + c
The equation of a straight line is given by:
Example
What is the equation of the straight line with gradient 3 that crosses the yaxis at y= 3 ?
Finding the intersection point between two straight lines
There are two types of problem here. One where the lines are not perpendicular to eachother and the other when they are.
To solve the former all that is needed is to solve the equations of the lines simultaneously.
With the later, only one equation is given and the second equation must be worked out from the information supplied. then it is a matter of proceding as before ie to solve the two equations simultaneously.
Example #1
Find the intersection point of the two straight lines:
Example #2
A straight line y = 2x + 4.5 intersects another perpendicularly. If the second straight line has an intercept of 0.5 on the yaxis, what are the coodinates of the point of intersection of the two lines? (answer to 1 d.p.)
Finding the eq. of a straight line from one point + gradient
Solution is by using the expression for gradient(m) for an actual point(x_{1},y_{1}) and a generalized point(x,y).
The straight line equation is found by substituting values of x_{1}, y_{1} and m into the above.
Example
A line of gradient 3 passes through a point (2,5). What is the equation of the line?
Finding the equation of a straight line from two points
Solution is by first finding the gradient m from the x and y values from the points (x_{1},y_{1}) and (x_{2},y_{2})
Then we use the expression again, but this time with one actual point and a generalized point(x,y).
The straight line equation is found by substituting for x_{1}, y_{1} and m.
Example
Find the equation of the line between the two points (2,3) and (5,7).

