SOLUTION: I really need some help with this problem: write the slope/intercept form of the equations of the lines described. 1. through: (-2,1) parallel to y=1/2x + 5 2. through:

Algebra ->  Functions -> SOLUTION: I really need some help with this problem: write the slope/intercept form of the equations of the lines described. 1. through: (-2,1) parallel to y=1/2x + 5 2. through:      Log On


   

Question 1003269: I really need some help with this problem:

write the slope/intercept form of the equations of the lines described.
1. through: (-2,1) parallel to y=1/2x + 5
2. through: (3, -5) perpendicular to y= 4/3x + 3
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
1. through: (-2,1) parallel to y=%281%2F2%29x+%2B+5

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 1%2F2 (its from the slope of y=%281%2F2%29%2Ax%2B5 which is also 1%2F2). Also since the unknown line goes through (-2,1), 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-1=%281%2F2%29%2A%28x%2B2%29 Plug in m=1%2F2, x%5B1%5D=-2, and y%5B1%5D=1



y-1=%281%2F2%29%2Ax-%281%2F2%29%28-2%29 Distribute 1%2F2



y-1=%281%2F2%29%2Ax%2B2%2F2 Multiply



y=%281%2F2%29%2Ax%2B2%2F2%2B1Add 1 to both sides to isolate y

y=%281%2F2%29%2Ax%2B2%2F2%2B2%2F2 Make into equivalent fractions with equal denominators



y=%281%2F2%29%2Ax%2B4%2F2 Combine the fractions



y=%281%2F2%29%2Ax%2B2 Reduce any fractions

So the equation of the line that is parallel to y=%281%2F2%29%2Ax%2B5 and goes through (-2,1) is y=%281%2F2%29%2Ax%2B2


So here are the graphs of the equations y=%281%2F2%29%2Ax%2B5 and y=%281%2F2%29%2Ax%2B2



graph of the given equation y=%281%2F2%29%2Ax%2B5 (red) and graph of the line y=%281%2F2%29%2Ax%2B2(green) that is parallel to the given graph and goes through (-2,1)





2. through: (3, -5) perpendicular to y=+%284%2F3%29x+%2B+3

Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line


Remember, any two perpendicular lines are negative reciprocals of each other. So if you're given the slope of 4%2F3, you can find the perpendicular slope by this formula:

m%5Bp%5D=-1%2Fm where m%5Bp%5D is the perpendicular slope


m%5Bp%5D=-1%2F%284%2F3%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%283%2F4%29 When you divide fractions, you multiply the first fraction (which is really 1%2F1) by the reciprocal of the second



m%5Bp%5D=-3%2F4 Multiply the fractions.


So the perpendicular slope is -3%2F4



So now we know the slope of the unknown line is -3%2F4 (its the negative reciprocal of 4%2F3 from the line y=%284%2F3%29%2Ax%2B3). Also since the unknown line goes through (3,-5), 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%2B5=%28-3%2F4%29%2A%28x-3%29 Plug in m=-3%2F4, x%5B1%5D=3, and y%5B1%5D=-5



y%2B5=%28-3%2F4%29%2Ax%2B%283%2F4%29%283%29 Distribute -3%2F4



y%2B5=%28-3%2F4%29%2Ax%2B9%2F4 Multiply



y=%28-3%2F4%29%2Ax%2B9%2F4-5Subtract -5 from both sides to isolate y

y=%28-3%2F4%29%2Ax%2B9%2F4-20%2F4 Make into equivalent fractions with equal denominators



y=%28-3%2F4%29%2Ax-11%2F4 Combine the fractions



y=%28-3%2F4%29%2Ax-11%2F4 Reduce any fractions

So the equation of the line that is perpendicular to y=%284%2F3%29%2Ax%2B3 and goes through (3,-5) is y=%28-3%2F4%29%2Ax-11%2F4


So here are the graphs of the equations y=%284%2F3%29%2Ax%2B3 and y=%28-3%2F4%29%2Ax-11%2F4




graph of the given equation y=%284%2F3%29%2Ax%2B3 (red) and graph of the line y=%28-3%2F4%29%2Ax-11%2F4(green) that is perpendicular to the given graph and goes through (3,-5)