SOLUTION: find the equation of the line passing through (-4,-3) and parallel to the line 3x+4y=12

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Question 668924: find the equation of the line passing through (-4,-3) and parallel to the line 3x+4y=12
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
the line passing through (-4,-3) and parallel to the line 3x%2B4y=12
write this equation in slope-intercept form:
4y=-3x%2B12
y=-%283%2F4%29x%2B3

first see the graph of the given line:

+graph%28+600%2C+600%2C+-10%2C10%2C+-10%2C+10%2C+-%283%2F4%29x%2B3%29+

here are both lines which are parallel to each other:
Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line


Since any two parallel lines have the same slope we know the slope of the unknown line is -3%2F4 (its from the slope of y=%28-3%2F4%29%2Ax%2B3 which is also -3%2F4). Also since the unknown line goes through (-4,-3), we can find the equation by plugging in this info into the point-slope formula

Point-Slope Formula:

y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope and (x%5B1%5D,y%5B1%5D) is the given point



y%2B3=%28-3%2F4%29%2A%28x%2B4%29 Plug in m=-3%2F4, x%5B1%5D=-4, and y%5B1%5D=-3



y%2B3=%28-3%2F4%29%2Ax%2B%283%2F4%29%28-4%29 Distribute -3%2F4



y%2B3=%28-3%2F4%29%2Ax-12%2F4 Multiply



y=%28-3%2F4%29%2Ax-12%2F4-3Subtract -3 from both sides to isolate y

y=%28-3%2F4%29%2Ax-12%2F4-12%2F4 Make into equivalent fractions with equal denominators



y=%28-3%2F4%29%2Ax-24%2F4 Combine the fractions



y=%28-3%2F4%29%2Ax-6 Reduce any fractions

So the equation of the line that is parallel to y=%28-3%2F4%29%2Ax%2B3 and goes through (-4,-3) is y=%28-3%2F4%29%2Ax-6


So here are the graphs of the equations y=%28-3%2F4%29%2Ax%2B3 and y=%28-3%2F4%29%2Ax-6



graph of the given equation y=%28-3%2F4%29%2Ax%2B3 (red) and graph of the line y=%28-3%2F4%29%2Ax-6(green) that is parallel to the given graph and goes through (-4,-3)