Question

Can somone pls explain what i did wrong, and the correct answer?? ( Parallel/Perpendicular Through Points algebra. write how to do questions like this simply.

Answer 1

The two linear equations are:

1)  y = -x + 5

2) y = (-1/2)*x - 1

How to get the linear equations?

Remember that two linear equations are parallel if and only if have the same slope and different y-intercept.

So to find a linear equation:

y = m*x + b

Parallel to:

x + y = 4

y = -x + 4

The slope needs to be m = -1 and the y-intercept b ≠ 4

So our line will be:

y = -x + b

To find the value of b, we use the fact that this line passes through (2, 3), replacing the values of the point in the line we get:

3 = -2 + b

3 + 2 = b

5 = b

The linear equation is y = -x + 5

For the second case, we want to find a line perpendicular to:

2x - y = 5

y = 2x - 5

Two lines are perpendicular if the product of the slopes is -1, then:

m*2 = -1

m = -1/2

So the perpendicular line is something like:

y = (-1/2)*x + b

To find the value of b we use the fact that this line needs to pass through (6, -4)

Replacing these values we get

-4 = (-1/2)*6 + b

-4 = -3 + b

-4 + 3  =b

-1 = b

The line is:

y = (-1/2)*x - 1

Learn more about linear equations:

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