Question

What is the equation of a line that passes through the point (4, 2) and is perpendicular to the line whose equation is y=x/3−1 ? Enter your answer in the box.

Answer 1

y = x/3 - 1....the slope here is 1/3. A perpendicular line will have a negative slope. All that means is flip the slope and change the sign. So our perpendicular line will have a slope of -3....see how I flipped 1/3 making it 3/1...and then I changed the sign...making it -3/1 or just -3

y = mx + b
slope(m) = -3
(4,2)...x = 4 and y = 2
now we sub into the formula and find b, the y int
2 = -3(4) + b
2 = -12 + b
2 + 12 = b
14 = b

so ur perpendicular equation is : y = -3x + 14

Answer 2

Lines can be parallel, perpendicular or have no relationship at all.

The equation of the line is: $\mathbf{y = -3x + 14}$

First, we calculate the slope of: $\mathbf{y = \frac x3 - 1}$

A linear equation is represented as:

$\mathbf{y = mx + c}$

Where:

m represents the slope

So, by comparison:

$\mathbf{m = \frac 13}$

From the question, we understand that the required line is perpendicular to $\mathbf{y = \frac x3 - 1}$

This means that, the slope (m2) of the required line is:

$\mathbf{m_2 = -\frac 1m}$

So, we have:

$\mathbf{m_2 = -\frac 1{1/3}}$

$\mathbf{m_2 = -3}$

The equation of the line is:

$\mathbf{y = m_2(x - x_1) + y_1)}$

Where:

$\mathbf{(x_1,y_1) = (4,2)}$

So, we have:

$\mathbf{y = -3(x - 4) + 2}$

Open bracket

$\mathbf{y = -3x + 12 + 2}$

$\mathbf{y = -3x + 14}$

Hence, the equation of the line is: $\mathbf{y = -3x + 14}$

Read more about equations of perpendicular lines at:

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