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)?

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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)?

Algebra
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|dw:1437711431685:dw| 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)
|dw:1437711852579:dw|
im not sure i understand

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Can you find the slope of the first line?
im confused with the whole thing, i dont understand any of it
Ok, are you familiar with this formula? |dw:1437712598401:dw|
Where m is slope of a line
yes!
Great! :-) Can you plug in the two points given for the first line to find the slope?
do you mean (-3,-4) & (0,-9) ?
Yep
is it y=5/3x-2 ?
Hm, I get the slope to be -5/3|dw:1437713469475:dw|
|dw:1437713498055:dw| this is what @JoannaBlackwelder tried to say... you need to susbstitute the values of x1, x2, y1, y2
And the slope of parallel lines is equal. :-)
So, the slope of the other line is also -5/3. Making sense so far?
was i close ?
Yes, but your slope was off.
Any ideas on finding the equation of the second line, using the slope of -5/3 and the point (3,-7)
okay one question, if a slope of a line is -1/2 the slope that is parallel to it would be -2 right?
or would it be just 2?
Parallel lines have the exact same slope
so it would be -1/2 ?
Right.
Perpendicular lines have negative reciprocal slopes is what I think you were thinking about before.
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)?
Sure, can you tell what the slope of the line given is?
m=2x ?
Close, just the 2 is the slope.
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.
okay how do i set up the equation?
We use the general formula y=mx+b
Plug in m, and the x and y coordinate we have
|dw:1437716031316:dw|
And solve for b
Can you find b?
2(2) would turn into 4x right? would i then divide that by -1 to get b?
Close
|dw:1437716846824:dw|
|dw:1437716867087:dw|
Make sense?
Yes ! that make sense!
Awesome! So then we can plug in m and b to make y=2x+(-6)
or y=2x-6
right !
:-D
thank you so much !!

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