Ineed with questions 4 and 5 on the math homework

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.

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