Expert: Josh - 12/2/2009

Question
write the equation of the line that passes through the given point and is parallel to the given line.

1. (1,-3),y =2x+2
2. (6,8),y =-5/2x+10
3. (5,-1),y= -3/5x-3

Write an equation of the line that passes through the given point and is parallel to the given line.

1. (5,4),y=3x+5
2.(-3,-7),y=-5x-2
3.(8,-3),y=3/4x+5

Answer
Hi Samantha,

As a general policy, we would like everyone to attempt the questions first before writing in to us. It is really important that you show some working because it gives the volunteer some idea of the difficulties you are experiencing. Without this knowledge, we sometimes answer the question correctly without really addressing the issues that most concern the reader.

Recall that a straight line equation may be written as y=m*x+b, where "m" is called the gradient, or the slope. Given the equation y=2x+2, any line parallel to it must have the same "m" value, i.e., m=2, in this case. Straight away, we know that the equation must be of the form y=2x+b. Now, the constant "b" which represents the point of intersection of the line with the y-axis, is the only unknown.

To find "b", we have to ensure the point (1,-3) which lies on the line satisfies the equation y=2x+b. Substituting x=1 and y=-3 into y=2x+b, we get -3=2*1+b, i.e., b=-5. So, the line which passes through (1,-3) and parallel to y=2x+2 is y=2x-5.

The same approach can be used for the other ones. For example, a line parallel to y =-5/2x+10 has the form y=-(5/2)x+b. If it passes through (6,8), then 8=(-5/2)*6+b, i.e., 8=-15+b, b-=23. Hence, the equation we need is y=(-5/2)x+23.

I shall leave you to complete the homework set yourself.