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=-\frac{3}{4}x+\frac{12}{3}$

you simplify:

$y=-\frac{3}{4}x+4$

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

$7=-\frac{3}{4}(-4)+b$

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:$y=-\frac{3}{4}x+4$