Question

write an equation of the line containing the given point and parallel to the given line.

(7,8); x+5y=2

(-2,4); 9x=5y+3

(3,5); 8x+y=2

(5,-3) 9x+4y=3

I am not sure how to do them

Answer 1

The key point to know is that:

if the new line is parallel, then the coefficients of x and y will be the same

(The coefficients are the numbers that x and y are multiplied by).

So, taking the first one, any line parallel to x+5y=2 will be of the form

x + 5y = some_number

x + 5y = -20

x + 5y = 3.14159

x + 5y = 0

are all parallel.

So to find the parallel line that goes through (7,8) we just have to find the specific number that makes such a line go through that point.

That point has x=7, y=8, so we need to plug those into the equation form that we know:

x + 5y = something

7 + 5 * 8 = something

7 + 47 = something = 47

So a line parallel to x+5y=2, containing (7,8) is x+5y=47.

Now try the others yourself.

Answer 2

I typoed, and it might confuse you. Sorry. 5*8 is 40, or course, not 47.

x + 5y = something

7 + 5 * 8 = something

7 + 40 = something = 47

So a line parallel to x+5y=2, containing (7,8) is x+5y=47.

Answer 3

I am so lost. i have to type my answers in point slope form (y=mx+b)

Answer 4

That's OK. First you solve it. Then you put it into the form you need.

Point slope form just means moving y to the left hand side, and everything else to the right.

Consider:

x + 5y = 47

Subtract x from both sides:

5y = 47 -x

Divide by 5

y = 47/5 - x/5

Answer 5

I am still lost sorry.

Answer 6

Take the next one then. Step by step.

9x = 5y + 3

Parallel, but going through (-2, 4).

x is -2. y is 4.

It must be

9x = 5y + something

9*-2 = 5*4 + something.

What is the something?

Answer 7

no idea