SOLUTION: 1. Find the equation of a line that is parallel to y= 2x-3 had has a y-intercept of 4 2. Find the equation of a line that is perpendicular y=-3x + 7 and has a y-intercept of -

Algebra ->  Linear-equations -> SOLUTION: 1. Find the equation of a line that is parallel to y= 2x-3 had has a y-intercept of 4 2. Find the equation of a line that is perpendicular y=-3x + 7 and has a y-intercept of -      Log On


   

Question 696671: 1. Find the equation of a line that is parallel to y= 2x-3 had has a y-intercept of 4

2. Find the equation of a line that is perpendicular y=-3x + 7 and has a y-intercept of -2


3. Find the equation of a line that is parallel to y =2x -1 and goes through the point(6,2)

4.Find the equation of a line that is perpendicular to y=1/3x + 2 and goes through the point (1,7)
Please work out all problems completely along with the solution.
Answer by MathLover1(20850) About Me  (Show Source):
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1. Find the equation of a line that is parallel to y=+2x-3 had has a y-intercept of 4 (means it passes through point (0,4))
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 2 (its from the slope of y=2%2Ax-3 which is also 2). Also since the unknown line goes through (0,4), 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-4=2%2A%28x-0%29 Plug in m=2, x%5B1%5D=0, and y%5B1%5D=4



y-4=2%2Ax-%282%29%280%29 Distribute 2



y-4=2%2Ax-0 Multiply



y=2%2Ax-0%2B4Add 4 to both sides to isolate y

y=2%2Ax%2B4 Combine like terms

So the equation of the line that is parallel to y=2%2Ax-3 and goes through (0,4) is y=2%2Ax%2B4


So here are the graphs of the equations y=2%2Ax-3 and y=2%2Ax%2B4



graph of the given equation y=2%2Ax-3 (red) and graph of the line y=2%2Ax%2B4(green) that is parallel to the given graph and goes through (0,4)





2. Find the equation of a line that is perpendicular y=-3x+%2B+7 and has a y-intercept of -2 (means it passes through point (0,-2))

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 (its from the slope of y=-3%2Ax%2B7 which is also -3). Also since the unknown line goes through (0,-2), 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%2B2=-3%2A%28x-0%29 Plug in m=-3, x%5B1%5D=0, and y%5B1%5D=-2



y%2B2=-3%2Ax%2B%283%29%280%29 Distribute -3



y%2B2=-3%2Ax-0 Multiply



y=-3%2Ax-0-2Subtract -2 from both sides to isolate y

y=-3%2Ax-2 Combine like terms

So the equation of the line that is parallel to y=-3%2Ax%2B7 and goes through (0,-2) is y=-3%2Ax-2


So here are the graphs of the equations y=-3%2Ax%2B7 and y=-3%2Ax-2



graph of the given equation y=-3%2Ax%2B7 (red) and graph of the line y=-3%2Ax-2(green) that is parallel to the given graph and goes through (0,-2)





3. Find the equation of a line that is parallel to y+=2x+-1 and goes through the point (6,2))

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 2 (its from the slope of y=2%2Ax-1 which is also 2). Also since the unknown line goes through (6,2), 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-2=2%2A%28x-6%29 Plug in m=2, x%5B1%5D=6, and y%5B1%5D=2



y-2=2%2Ax-%282%29%286%29 Distribute 2



y-2=2%2Ax-12 Multiply



y=2%2Ax-12%2B2Add 2 to both sides to isolate y

y=2%2Ax-10 Combine like terms

So the equation of the line that is parallel to y=2%2Ax-1 and goes through (6,2) is y=2%2Ax-10


So here are the graphs of the equations y=2%2Ax-1 and y=2%2Ax-10



graph of the given equation y=2%2Ax-1 (red) and graph of the line y=2%2Ax-10(green) that is parallel to the given graph and goes through (6,2)




4.Find the equation of a line that is perpendicular to y=%281%2F3%29x+%2B+2 and goes through the point (1,7))

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%2F3 (its from the slope of y=%281%2F3%29%2Ax%2B2 which is also 1%2F3). Also since the unknown line goes through (1,7), 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-7=%281%2F3%29%2A%28x-1%29 Plug in m=1%2F3, x%5B1%5D=1, and y%5B1%5D=7



y-7=%281%2F3%29%2Ax-%281%2F3%29%281%29 Distribute 1%2F3



y-7=%281%2F3%29%2Ax-1%2F3 Multiply



y=%281%2F3%29%2Ax-1%2F3%2B7Add 7 to both sides to isolate y

y=%281%2F3%29%2Ax-1%2F3%2B21%2F3 Make into equivalent fractions with equal denominators



y=%281%2F3%29%2Ax%2B20%2F3 Combine the fractions



y=%281%2F3%29%2Ax%2B20%2F3 Reduce any fractions

So the equation of the line that is parallel to y=%281%2F3%29%2Ax%2B2 and goes through (1,7) is y=%281%2F3%29%2Ax%2B20%2F3


So here are the graphs of the equations y=%281%2F3%29%2Ax%2B2 and y=%281%2F3%29%2Ax%2B20%2F3



graph of the given equation y=%281%2F3%29%2Ax%2B2 (red) and graph of the line y=%281%2F3%29%2Ax%2B20%2F3(green) that is parallel to the given graph and goes through (1,7)