Question

Consider the line y=−4x+2.

Find the equation of the line that is perpendicular to this line and passes through the point , (−3,5).

Find the equation of the line that is parallel to this line and passes through the point , (−3, 5).
equation of perpendicular line:
equation of parallel line:

Answer 1

Answer and step by step esplanation:

The perpendicular line has the slope opposite and inverse, in our case
`-4 \rightarrow +\frac14`

Line passing through the point will have then equation - using the point-slope form
`y-y_0=m(x-x_0)`

`y-5=\frac14 (x-(-5))\\y-5=\frac14(x+5)`

The parallel line will have the same slope as the given line, in our case -4. Again with the point-slope equation:

`y-5=-4(x-(-5)\\y-5=-4(x+5)`

Answer 2

Perpendicular: y = 1/4x + 5 3/4

Parallel: y = -4x - 7

Explanation:

Hello!

A perpendicular line would have a negative reciprocal slope, meaning you flip the sign of the slope, and the numerator and denominator.

Perpendicular Line

Given our equation: y = -4x + 2, we can find the perpendicular slope by finding the negative reciprocal:

• -4
• 4 -> negative
• 1/4 -> reciprocal (4/1 -> 1/4)

So the perpendicular slope is 1/4.

We can now solve for the y-intercept by plugging in the x and y-value of the point into the equation y = 1/4x + b:

• y = 1/4x + b; (-3,5)
• 5 = 1/4(-3) + b
• 5 = -3/4 + b
• b = 5 3/4.

The y-intercept is 5 3/4, so the equation of the line would be y = 1/4x + 5 3/4.

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Parallel Line

Parallel lines have the same slope. So we can use -4 as our slope, and plug in the points to find the y-intercept.

• y = -4x + b; (-3,5)
• 5 = -4(-3) + b
• 5 = 12 + b
• -7 = b

So the equation of the parallel line would be y = -4x - 7.