Math CentralQuandaries & Queries


Question from vince, a student:

write an equation of the line satisfying the given conditions
Through (2,-3) parallel to 2x=3y+5 and graph both equations

So far I did

-3y= 2x+5


y-(-3) 2/3(x-2)

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

y= 2/3

can you show what else I would do or how I would do it

Hi Vince,

You have the right idea but you need to sharpen your algebraic skills. If you can put the line in the form

y = mx + b

that is y equals a number times x plus a number, then m is the slope of the line. That will be helpful since any parallel line has the same slope. So how do you put the equation of the line in the correct form?

You want y on the left of the equal sign so rewrite the equation

2x = 3y + 5


3y + 5 = 2x

But you don't want the 5 on the left side so add -5 to both sides. This gives

3y + 5 - 5 = 2x - 5 or
3y = 2x - 5

Almost there. Divide both sides by 3 to get

3y/3 = 2x/3 - 5/3 or
y = 2/3 x - 5/3

Thus the line has slope 2/3 and so the parallel line you want also has slope 2/3. Hence the line you are looking for has the form

y = 2/3 x - b             (1)

for some number b.

You know one other fact, the point (2, -3) is on the line. Hence substitute x = 2 and y = -3 into the equation (1) and solve for b.

I hope this helps,

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