Question

Can anyone help me with these 4 questions i havw no idea what to do

Answer 1

Consider the problem 15. We have the point (5,-4) and the line y=(1/5)x-4 and we want the equation of a line that passes through the given point that is parallel to the given line. Recall that the general equation of a line is of the form y=mx+b where m is the slope and b is the y intercept. Also, have in mind that two lines are parallel if and only if they have the same slope. Let us have the equation we are looking for as y=mx+b. Since this line must be parallel to the line y=(1/5)x-4 it must happen that they have the same slope. For the line y=(1/5)x-4 the slope is (1/5). Then the slope of the line we are looking for is also (1/5).

Now, we should determine the value of b. So far we have this expression

`y=(1)/(5)\cdot x+b`

We want this line to pass through the point (5,-4). So, this means that whenever we replace x by 5, we should also replace y by -4. This gives us the equation

`-4=(1)/(5)\cdot5+b`

which is the equation

`b+1=-4`

by subtracting 1 on both sides, we get

`b=-4-1=-5`

So the equation of our line would be

`y=(1)/(5)x-5`