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netineya [11]
2 years ago
13

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.
Mathematics
1 answer:
mote1985 [20]2 years ago
8 0

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)

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