Question

What is the equation of the line that passes through the point (4.11) and is perpendicular to the line with the following equation? OA. y = -x + 14 O B. - r - 15 OD. & 1 + 8​

Answer 1

Answer:

$y = x +7$

Step-by-step explanation:

Given

$Point\ (x_1,y_1) = (4,11)$

Perpendicular to $y = -x + 14$

Required

Determine the line equation

An equation has the form

$y = mx + b$

Where

$m = slope$

By comparison with $y = -x + 14$

$m = -1$

Because the line is perpendicular to $y = -x + 14$, the following relationship exists

$m_1 = \frac{-1}{m}$ i.e. the condition for perpendicularity

Where m1 is the slope of the equation that passes through $Point\ (x_1,y_1) = (4,11)$

So, we have:

$m_1 = \frac{-1}{-1}$

$m_1 = 1$

The line equation is then calculated using:

$y - y_1 = m_1(x - x_1)$

Where

$m_1 = 1$

$Point\ (x_1,y_1) = (4,11)$

So, we have:

$y - 11 = 1(x - 4)$

$y - 11 = x - 4$

Add 11 to both sides

$y - 11+11 = x - 4+11$

$y = x - 4+11$

$y = x +7$

The B, C and D parts of your question are not clear.

Apply the same steps used in (a) above and you'll get your answers