Question

Need HELP!!!! Write the point-slope form of the line that passes through (5, 5) and is perpendicular to a line with a slope of 1/4. Include all of your work in your final answer.

Answer 1

Answer:

$y - 5 = -4(x-5)$

Step-by-step explanation:

Given

Line coordinates: (5,5)

Perpendicular slope = $\frac{1}{4}$

Required

Find the point slope form of the line

First, the slope of the line has t be calculated;

Given that two lines are perpendicular;

The relationship between there slopes is given as $m_1.m_2 = -1$

Let m_2 represent the slope of the second line;

such that $m_2 = \frac{1}{4}$

So;

$m_1 * \frac{1}{4} = -1$

Multiply both sides by 4

$m_1 * \frac{1}{4} * 4 = -1 * 4$

$m_1 = -1 * 4$

$m_1 = -4$

Now, the equation of the line can be calculated using slope formula;

$m = \frac{y - y_1}{x- x_1}$

Where

$(x_1,y_1) = (5,5)\\m_1 =m = -4$

So; $m = \frac{y - y_1}{x- x_1}$ becomes

$-4 = \frac{y - 5}{x- 5}$

Multiply both sides by x - 5

$-4(x-5) = \frac{y - 5}{x- 5} * (x-5)$

$-4(x-5) = y - 5$

Reorder

$y - 5 = -4(x-5)$

Hence, the line in point-slope form is $y - 5 = -4(x-5)$