Question

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)

Answer 1

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`