Question

Can someone please help me with #14 and #15?

14.Given y=2(x - 10)+3, write an equation in point slope and slope intercept form that is:

a) Parallel and goes through (-4,1).

b) Perpendicular and goes through (-4,1).


15.Given 5x+2y=7

a.Find an equation parallel to the equation and through (0,10).


b.Find an equation perpendicular to the equation and through (0,10).

This picture is an example of what the answers should look like.​

Answer 1

Problem 14, Part (a)

The given equation y = 2(x-10)+3 has a slope of m = 2. Anything parallel to this will also have the same slope, but a different y intercept.

Let's find the point slope form of the parallel line through (-4,1)

$y-y_1 = m(x - x_1)\\\\y-1 = 2(x - (-4))\\\\y-1 = 2(x + 4)$

The point slope form is:  y-1 = 2(x+4)

Now solve for y to get the slope intercept form.

$y-1 = 2(x + 4)\\\\y = 2(x + 4)+1\\\\y = 2x + 8+1\\\\y = 2x + 9$

The slope intercept form is:  y = 2x+9

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Problem 14, Part (b)

The original slope is m = 2. Apply the negative reciprocal to go from 2/1 to -1/2. The perpendicular slope is -1/2.

Using the same point (-4,1), we find that the point slope form is...

$y-y_1 = m(x - x_1)\\\\y-1 = -\frac{1}{2}(x - (-4))\\\\y-1 = -\frac{1}{2}(x+4)$

The point slope form is:  y-1 = (-1/2)*(x+4)

Now solve for y

$y-1 = -\frac{1}{2}(x+4)\\\\y = -\frac{1}{2}(x+4)+1\\\\y = -\frac{1}{2}x-2+1\\\\y = -\frac{1}{2}x-1$

The slope intercept form is:  y = (-1/2)x - 1

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Problem 15, Part (a)

Anything parallel to Ax+By = C will be in the form Ax+By = D. The only thing changes is the C becomes D, where $C \ne D$. If C = D, then we'd be talking about the exact same line rather than two parallel lines.

We're given 5x+2y = 7. The answer is in the form 5x+2y = D. Plug in (x,y) = (0,10) to find the value of D

5x+2y = D

D = 5x+2y

D = 5(0)+2(10)

D = 20

The equation 5x+2y = D updates to 5x+2y = 20

Answer:  5x+2y = 20

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Problem 15, Part (b)

If you are given Ax+By = C, then anything perpendicular to this is Bx-Ay = D. Here it's possible that C = D; however, it's likely that they'll be different.

The given equation 5x+2y = 7 is perpendicular to anything of the form 2x-5y = D. We'll plug in the given point to find D.

2x-5y = D

D = 2x-5y

D = 2(0)-5(10)

D = -50

Answer:  2x-5y = -50