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Determine if the following equations are parallel, perpendicular, or neither. 7(x – 1) = 3y + 21 and 3.5x + 1.5y = 4.5

User John Smith Optional
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1 Answer

19 votes
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Given the two equations

7(x - 1) = 3y + 21

3.5x + 1.5y = 4.5

To determine if the lines are visible or perpendicular

Step 1: Expand the equations and make y the subject of the formula

7(x - 1) = 3y + 21

=> 7x - 7 = 3y + 21

=> 3y = 7x - 7 - 21

=> 3y = 7x -28

Divide both sides by 3

y = 7/3x - 28/3 ------equation 1

3.5x + 1.5y = 4.5

1.5y = -3.5x + 4.5

Divide both sides by 1.5

y = -3.5/1.5 x + 4.5/1.5

y = -7/3x + 3--------equation 2

Step 2: compare the two equations to the equation of a line, y = mx + c

For equation 1

m = 7/3

For equation 2

m= -7/3

The slopes are not the same

Also, the product of the gradients did not give -1

It can be seen that the lines are neither perpendicular nor parallel

User Bastaspast
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