Question

Write an equation for the line that passes through the given point and is parallel/perpendicular to the graph of the given point.
Parallel: Y=3x-2; (3,2)
Perpendicular: Y= -2x-1; (2,-1)

Also I will mark brainly to who explain what they did step by step

Answer 1

Answer:

Parallel: The slope is the same as in the previous equation. So, y=3x+b. To find the value of b, you plug in the given point, 2=3(3)+b, b=-7. So the equation is y=3x-7.

Perpendicular: The slope is the negative reciprocal when an equation is perpendicular. The negative reciprocal of -2 is 1/2. So, y=1/2x+b. To find the value of b, you plug in the given point, -1=1/2(2)+b, -1=1+b, b=-2. So the equation is y=1/2x-2.

:)

Answer 2

9514 1404 393

Answer:

• parallel: y = 3x -7
• perpendicular: y = 1/2x -2

Step-by-step explanation:

The given line equations are written in "slope-intercept" form.

  y = mx + b . . . . . . . . . m is the slope; b is the y-intercept

If we solve this equation for b, we find ...

  b = y - mx

This is useful for completing the equation of the line through a given point when the slope is known.

Parallel

A parallel line will have the same slope as the given line. The given line has a slope (x-coefficient) of 3. We can find the "b" of the line through the desired point as ...

  b = y -3x

  b = 2 -(3)(3) = -7

The equation of the parallel line is ...

  y = 3x -7

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Perpendicular

A perpendicular line will have a slope that is the opposite reciprocal of the slope of the line it is perpendicular to. Here, the given line has a slope of -2, so the perpendicular line will have a slope of ...

  -1/(-2) = 1/2

Then the y-intercept is ...

  b = y -(1/2)x

  b = -1 -(1/2)(2) = -2

And the equation of the perpendicular line is ...

  y = 1/2x -2

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The attached graph shows the original lines as dashed lines, and the corresponding desired lines as solid lines in the same color.