Question 4
Recall the following facts:
1. If two lines are parallel, their slopes are the same
2. If two lines are perpendicular, the product of their slopes equals 1.
The line given to us is:
By comparing to ;
The slope is
Now let us compare this to:
which has slope
Now let us check to see if the two are parallel,
Since the two slopes are not the same, they are not parallel.
Now let us check to see if they are perpendicular
Since their product is not -1, the two lines are not perpendicular.
Hence ,
is neither parallel or perpendicular to
The next equation is
The slope of this equation is
Since,
The equation
is perpendicular to
The next equation is
Since the slope if the two are equal, that is
the two equations are parallel.
The next equation is
Since
the two equations are perpendicular.
Question 5.
The given line in the graph passes through,
(10,7), (-8,-5) and (1,1).
Using any two points we can determine the slope,
The line parallel to this line which passes through (5,-1), also has slope
The equation of this line is
This implies that,
This simplifies to
To find any point on this line, choose any value for x and solve the corresponding y value. So when
Hence
is a point on this line.