Write an equation of the line that passes through (7,10) and is perpendicular to the line y=12x−9.

Answer 1

Hi...

PERPENDICULAR lines have slopes whose product will be - 1. That is m1•m2 = -1 and one is the NEGATIVE RECIPROCAL of the other.

So if the given has a slope, m = 12 (since y = 12x - 9)...then the slope of the line you want the equation for will be -¹/₁₂

Use the POINT-SLOPE formula and plug into the values for the ordered point given (7, 10)

y - y₁ = m(y - x₁)

y - 10 = -¹/₁₂ (x - 7)

y - 10 = -¹/₁₂ (x) + ⁷/₁₂

y = -¹/₁₂ (x) + ⁷/₁₂ + 10

y = -¹/₁₂ (x) + ¹²⁷/₁₂ Final answer

Answer 2

Here is the solution to a similar problem though the original line and point are different. Just read through my explanation carefully until you understand it, and you will be able to solve your problem and any other problem similar to it.

First, write the given line in slope-intercept form, which means that it has y by itself on one side of the equals sign.

2y + 4x = 12

—4x –4x [Subtracting 4x from each side]

2y = 12 — 4x

2y = 12 — 4x

---- ------------- [Dividing each side by 2]

2 2

y = 6 – 2x [Next, I am going to switch the order of the terms on the left: commutative property of addition]

y = –2x + 6 [This is in slope-intercept format.]

The SLOPE of this line is the coefficient of the x, that is, the number multiplied by x. So, the slope of your given line is —2.

Every line perpendicular to your given line has a related, but NOT the same, slope. The perpendicular lines to your given line have the slope 1/2; you get that by changing the sign of your original slope and then taking the reciprocal. The original slope was —2 or —2/1; the slope of your perpendicular line will be +1/2.

Remember: Parallel lines all have the same slope as each other. Perpendicular lines have slopes that are the negative reciprocal of each other.

Now you start building the equation of the perpendicular line in question.

So far, we have: y = 1/2 x + c

We only have to calculate c, a constant, and we will be done.

What we do is plug in the specific values for x and y from the point that you were given, (8,1). The fact that this point is on the line means that it makes the above equation that we are building TRUE, so :

1 = 1/2(8) + c

We have one equation in one unknown (c), and we will solve for that one unknown..

1 = 1/2(8) + c

1 = 4 + c

1 — 4 = 4 — 4 + c [Subtracting 4 from each side]

—3 = c

We have c. Now go back to our semi-finished equation for the perpendicular line (y = 1/2 x + c) and fill in the value for c that we have calculated to get:

y = 1/2 x — 3

This is your equation for the one line that contains (1,8) and also is perpendicular to your original line.