Mathematics, 06.01.2021 14:50 Anthonyc123

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Answer from: crystrow9p6qc7n

Equation of Parallel line: y = -5x-34Equation of Perpendicular line: y = 1/5x - 14/5

Step-by-step explanation:

a) Equation of Parallel line to the given line and passes through the point (-6, -4)

We know that the slope-intercept form of the line equation is

y = mx+b

where m is the slope and b is the y-intercept

Given the line

y = -5x+4

comparing with the slope-intercept form of the line equation

The slope of the line = m = -5

We know that parallel lines have the same slope. Thus, the slope of the line parallel to the line y = -5x+4 will also be: -5

So, the equation of the line parallel to the given line and passes through the point (-6, -4) will be:

Using the point-slope form of the line equation

$y-y_1=m\left(x-x_1\right)$

where m is the slope of the line and (x₁, y₁) is the point

substituting the values m = -5 and the point (-6, -4)

y - (-4) = -5(x-(-6))

y+4 = -5(x+6)

y+4 = -5x-30

y = -5x-30-4

y = -5x-34

Therefore, the the equation of the line parallel to the given line and passes through the point (-6, -4) will be:

y = -5x-34

Hence:

Equation of Parallel line: y = -5x-34

a) Equation of Parallel line to the given line and passes through the point (-6, -4)

Given the line

y = -5x+4

comparing with the slope-intercept form of the line equation

The slope of the line = m = -5

We know that a line to perpendicular another line contains a slope that is the negative reciprocal of the slope of the other line, such as:

The slope of new line = – 1/m = -1/-5 = 1/5

So, the equation of the line perpendicular to the given line and passes through the point (-6, -4) will be:

Using the point-slope form of the line equation

$y-y_1=m\left(x-x_1\right)$

where m is the slope of the line and (x₁, y₁) is the point

substituting the values m = 1/5 and the point (-6, -4)

y - (-4) = 1/5 (x-(-6))

y+4 = 1/5 (x+6)

Subtract 4 from both sides

$y+4-4=\frac{1}{5}\left(x+6\right)-4$

$y=\frac{1}{5}x-\frac{14}{5}$

Therefore, the equation of the line perpendicular to the given line and passes through the point (-6, -4) will be:

$y=\frac{1}{5}x-\frac{14}{5}$

Hence:

Equation of Perpendicular line: y = 1/5x - 14/5

Answer from: Quest

step-by-step explanation:

Patrick is responsible for choosing a company his local community group will use for having t-shirts

Answer from: Quest

question: how many people can she serve?

answer: she can serve 16.66666667 people. so she can only give 16 people a complete serving.

question: does she have enough ice cream for her guests?

answer: no. explanation: she only has enough for 16 people to have a full serving. however, she can give a 17th person a partial serving.

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