Question

Write the equation of the line that is parallel to the line 4x − 3y = −12 and passes through the point (−3, 4).

y = four thirdsx + 8

y = four thirdsx + 3

y = −three fourthsx + 8

y = −three fourthsx + 3

Answer 1

First you should be able to write the given equation of the line in the slope intercept form(i.e y=mx + b....m being the slope and b being the intercept)

so, 4x-3y=-12 is the same as y=4/3x+4 (writing the given equation interms of y) from the slope intercept form of the above equation the slope is 4/3.
and for two lines to be parallel the should have the same slope so the equation of the new line that is parallel to our original line is also
4/3.now,to find the equation of this line we are given the point (-3,4) and to work this out we use the point slope form of equation of a line(which is of the form (y-b)=m(x-a) such that (a,b) is a pont on the line)
since we know a point on the line and of course its slope,the equation of the line is.. y-4=4/3(x-(-3)) is the same as y-4=4/3(x+3) from your choices I see that the equation of this line must be in its slope intercpet form. y-4=4/3(x+3) is the same as y=4/3(x+3)+4 (I added 4 to both sides of the equation) y=4/3x + (4/3)3 + 4 y=4/3x + 4 +4 y=4/3x + 8 is the equation of the line which is parallel to the line 4x - 3y=-12 and passing through the point (-3,4)



Additional points.
Remember that perpendicular lines have slopes of negative reciprocals of one anoter say if the slope of one line is 4/3 the slope of the perpendicular line to this line is its negative reciprocal which is -3/4