MATH SOLVE

4 months ago

Q:
# What is the equation of the line that is perpendicular to the given line and passes through the point (5, 3)? Please explain how you get your answer.4x - 5y = 55x + 4y = 374x + 5y = 55x - 4y = 8

Accepted Solution

A:

The equation for the graph of the picture isΒ

y = -5/4x

The slope of the perpendicular line needs to be the reciprocal of the other. To get reciprocal, switch the numerator and denominator with each other and flip the sign.

-5/4 β 4/-5 β 4/+5, or 4/5.

y = 4/5x + b

Input the coordinate point values and solve for b.

3 = 4/5(5) + b

Simplify.

3 = 4 + b

Subtract 4 from both sides.

-1 = b

y = 4/5x - 1

Now, we must convert this into Standard Form. It cannot contain any fractions and A, or the first number, cannot be negative.

y = 4/5x - 1

Subtract 4/5x from both sides.

-4/5x + y = -1

Multiply everything by -5 to make A positive and a whole number.

4x - 5y = 5

The first option is correct.

y = -5/4x

The slope of the perpendicular line needs to be the reciprocal of the other. To get reciprocal, switch the numerator and denominator with each other and flip the sign.

-5/4 β 4/-5 β 4/+5, or 4/5.

y = 4/5x + b

Input the coordinate point values and solve for b.

3 = 4/5(5) + b

Simplify.

3 = 4 + b

Subtract 4 from both sides.

-1 = b

y = 4/5x - 1

Now, we must convert this into Standard Form. It cannot contain any fractions and A, or the first number, cannot be negative.

y = 4/5x - 1

Subtract 4/5x from both sides.

-4/5x + y = -1

Multiply everything by -5 to make A positive and a whole number.

4x - 5y = 5

The first option is correct.