Hi Lisa,

If you have the equation of a line in the form y = mx + b then you know immediately that the slope of the line is m. Similarly if you know that a line has slope m then you know that there is a number b so that the equation of the line can be written y = mx + b.

I'm going to solve a problem that is similar to yours.

Write an equation of the line containing the given points and parallel to the given line.
Express the answer in the form of y = mx + b.
(2, 3); 3x + 4y = -5.

I am going to first write the equation 3x + 4y = -5 in the form y = mx + b since that will tell me the slope.

3x + 4y = -5

add -3x to both sides

4y = -3x - 5

divide both sides by 4

y = -3/4 x - 5/4.

This is in the required form y = mx + b so I know that m = -3/4 is the slope of the given line.

Parallel lines have the same slope so the line I am seeking also has slope m = -3/4. Thus there is some number b so that the line I want is y = -3/4 x + b. All that remains is to find b.

The extra fact I know is that the point (2, 3) is on this line, so substituting x = 2, y = 3 I get

3 = -3/4 (2) + b

and hence

b = 3 + 3/2 = 9/2.

Hence the equation of the line parallel to 3x + 4y = -5 and containing (2, 3) is

y = -3/4 x + 9/2.

Now you try your question.

Penny