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what is the equation for the line that passes through the given point and is parallel to the graph of 3x+4y=12; (-4,7)

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Two parallel lines have the same slope.

Then, if you have the line:


3x+4y=12

You need to identify the slope in this equation to know the slope of the line parallel to it. To find the slope you can turn the equation to slope-intercept form (y=mx+b) by clearing the variable y:


4y=-3x+12
y=-(3)/(4)x+(12)/(3)

you simplify:


y=-(3)/(4)x+4

The slope in the equation above is m= - 3/4

Then the slope of the equaion you need to find is -3/4

You use the given point to find the value of the b (in the slope-intercept form of the line equation):


y=mx+b

( -4 , 7)

m= -3/4

y= 7

x= -4


7=-(3)/(4)(-4)+b

You make the operations:


7=3+b

and clear the b:


b=7-3=4

You know the value of m and b.

Then, the equation is:
y=-(3)/(4)x+4

User Mraron
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