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Question 134107: Using the information provided, find the parallel and the perpendicular equation. Graph all three equations on a grid.
1. Y=4x+8 (2,5)
Parallel equation:
Perpendicular equation
2. y=3x-5 (6,9)
Parallel equation:
Perpendicular equation:
3. y=-5x+3 (-2,-3)
parallel equation:
Perpendicular equation:
Answer by algebrapro18(249)   (Show Source):
You can put this solution on YOUR website! To do these you need to know that parallel lines have the same slope and that perpendicular lines have opposite reciprocal slopes.
1. Y=4x+8 (2,5)
Parallel equation: y = 4x-3
well since the slope of the original line was 4 the parallel line will also have a slope of 4. Now we can find the equation of this line two ways.
Method 1: using y=mx+b and solving for b.
we know that y = 5 and m = 4 and x =2 from the given information so now we just need to calculate b.
y=mx+b
5 = 4*2 + b
5 = 8 + b
-3 = b
now we just back into the y=mx+b form and the equation of the line becomes:
y = 4x-3
Method 2: Using point-slop formula
we know that y1 = 5 and m = 4 and x1 = 2 so now we can put this into the point slope formula and solve for y.
y-y1=m(x-x1)
y - 5 = 4(x-2)
y -5 = 4x-8
y= 4x-3
either method gives the same answer.
Perpendicular equation: y = -1/4x+11/2
well since the slope of the original line was 4 the perpendicular line will have a slope of -1/4. Now we can find the equation of this line two ways.
Method 1: using y=mx+b and solving for b.
we know that y = 5 and m = -1/4 and x =2 from the given information so now we just need to calculate b.
y=mx+b
5 = (-1/4)*2 + b
5 = -1/2 + b
11/2 = b
now we just back into the y=mx+b form and the equation of the line becomes:
y = -1/4x+11/2
Method 2: Using point-slop formula
we know that y1 = 5 and m = -1/4 and x1 = 2 so now we can put this into the point slope formula and solve for y.
y-y1=m(x-x1)
y - 5 = -1/4(x-2)
y -5 = -1/4x+1/2
y= -1/4x+11/2
either method gives the same answer.
2. y=3x-5 (6,9)
Parallel equation: y = 3x-9
well since the slope of the original line was 3 the parallel line will also have a slope of 3. Now we can find the equation of this line two ways.
Method 1: using y=mx+b and solving for b.
we know that y = 9 and m = 3 and x =6 from the given information so now we just need to calculate b.
y=mx+b
9 = 3*6 + b
9 = 18 + b
-9 = b
now we just back into the y=mx+b form and the equation of the line becomes:
y = 3x-9
Method 2: Using point-slop formula
we know that y1 = 9 and m = 3 and x1 = 6 so now we can put this into the point slope formula and solve for y.
y-y1=m(x-x1)
y - 9 = 3(x-6)
y -9 = 3x-18
y= 3x-9
either method gives the same answer.
Perpendicular equation: y = -1/3x+11
well since the slope of the original line was 3 the perpendicular line will have a slope of -1/3. Now we can find the equation of this line two ways.
Method 1: using y=mx+b and solving for b.
we know that y = 9 and m = -1/3 and x = 6 from the given information so now we just need to calculate b.
y=mx+b
9 = (-1/3)*6 + b
9 = -2 + b
11 = b
now we just back into the y=mx+b form and the equation of the line becomes:
y = -1/3x+11
Method 2: Using point-slop formula
we know that y1 = 9 and m = -1/3 and x1 = 6 so now we can put this into the point slope formula and solve for y.
y-y1=m(x-x1)
y - 9 = -1/3(x-6)
y -9 = -1/3x + 2
y= -1/3x + 11
either method gives the same answer.
3. y=-5x+3 (-2,-3)
parallel equation: y = -5x-13
well since the slope of the original line was -5 the parallel line will also have a slope of -5. Now we can find the equation of this line two ways.
Method 1: using y=mx+b and solving for b.
we know that y = -3 and m = -5 and x = -2 from the given information so now we just need to calculate b.
y=mx+b
-3 = -5*-2 + b
-3 = 10 + b
-13 = b
now we just back into the y=mx+b form and the equation of the line becomes:
y = -5x-13
Method 2: Using point-slop formula
we know that y1 = -3 and m = -5 and x1 = -2 so now we can put this into the point slope formula and solve for y.
y-y1=m(x-x1)
y + 3 = -5(x+2)
y + 3 = -5x-10
y= -5x-13
either method gives the same answer.
Perpendicular equation: y = 1/5x-13/5
well since the slope of the original line was -5 the perpendicular line will have a slope of 1/5. Now we can find the equation of this line two ways.
Method 1: using y=mx+b and solving for b.
we know that y = -3 and m = 1/5 and x = -2 from the given information so now we just need to calculate b.
y=mx+b
-3 = (1/5)*-2 + b
-3 = -2/5 + b
-13/5 = b
now we just back into the y=mx+b form and the equation of the line becomes:
y = 1/5x-13/5
Method 2: Using point-slop formula
we know that y1 = -3 and m = 1/5 and x1 = -2 so now we can put this into the point slope formula and solve for y.
y-y1=m(x-x1)
y + 3 = 1/5(x+2)
y +3 = 1/5x + 2/5
y= 1/5x -13/5
either method gives the same answer.
I will leave the graphing to you.
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