A line passes through the point (–3, –4) and its y-intercept is (0, –9). What is the equation of the line that is parallel to the first line and passes through the point (3, –7)?

- anonymous

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- midhun.madhu1987

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First find the Slope of the First Line using the formula: Slope, m = (y2-y1)/(x2-x1)
The slope of second line and first line will be Equal. Because parallel lines have equal slope.
once you get the slope of second line, the equation can be written :
y - y1 = m(x - x1)

- midhun.madhu1987

|dw:1437711852579:dw|

- anonymous

im not sure i understand

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## More answers

- JoannaBlackwelder

Can you find the slope of the first line?

- anonymous

im confused with the whole thing, i dont understand any of it

- JoannaBlackwelder

Ok, are you familiar with this formula?
|dw:1437712598401:dw|

- JoannaBlackwelder

Where m is slope of a line

- anonymous

yes!

- JoannaBlackwelder

Great! :-) Can you plug in the two points given for the first line to find the slope?

- anonymous

do you mean (-3,-4) & (0,-9) ?

- JoannaBlackwelder

Yep

- anonymous

is it y=5/3x-2 ?

- JoannaBlackwelder

Hm, I get the slope to be -5/3|dw:1437713469475:dw|

- midhun.madhu1987

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this is what @JoannaBlackwelder tried to say... you need to susbstitute the values of x1, x2, y1, y2

- JoannaBlackwelder

And the slope of parallel lines is equal. :-)

- JoannaBlackwelder

So, the slope of the other line is also -5/3. Making sense so far?

- anonymous

was i close ?

- JoannaBlackwelder

Yes, but your slope was off.

- JoannaBlackwelder

Any ideas on finding the equation of the second line, using the slope of -5/3 and the point (3,-7)

- anonymous

okay one question, if a slope of a line is -1/2 the slope that is parallel to it would be -2 right?

- anonymous

or would it be just 2?

- JoannaBlackwelder

Parallel lines have the exact same slope

- anonymous

so it would be -1/2 ?

- JoannaBlackwelder

Right.

- JoannaBlackwelder

Perpendicular lines have negative reciprocal slopes is what I think you were thinking about before.

- anonymous

could you help with this one as well? The equation of a line is y = 2x + 3. What is the equation of the line that is parallel to the first line and passes through (2, –1)?

- JoannaBlackwelder

Sure, can you tell what the slope of the line given is?

- anonymous

m=2x ?

- JoannaBlackwelder

Close, just the 2 is the slope.

- JoannaBlackwelder

Now, we need to use that slope since the lines are parallel and the point (2,-1) to find the new equation of the line.

- anonymous

okay how do i set up the equation?

- JoannaBlackwelder

We use the general formula
y=mx+b

- JoannaBlackwelder

Plug in m, and the x and y coordinate we have

- JoannaBlackwelder

|dw:1437716031316:dw|

- JoannaBlackwelder

And solve for b

- JoannaBlackwelder

Can you find b?

- anonymous

2(2) would turn into 4x right? would i then divide that by -1 to get b?

- JoannaBlackwelder

Close

- JoannaBlackwelder

|dw:1437716846824:dw|

- JoannaBlackwelder

|dw:1437716867087:dw|

- JoannaBlackwelder

Make sense?

- anonymous

Yes ! that make sense!

- JoannaBlackwelder

Awesome! So then we can plug in m and b to make
y=2x+(-6)

- JoannaBlackwelder

or y=2x-6

- anonymous

right !

- JoannaBlackwelder

:-D

- anonymous

thank you so much !!

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