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Lina20 [59]
3 years ago
7

(20,-8); 7x - 4y = -5

Mathematics
1 answer:
ipn [44]3 years ago
8 0

The question is incomplete.

However, from the given parameters, a likely question could be to:

1. Write an equation in slope intercept form through (20,-8) and is parallel to 7x - 4y = -5

or

2. Write an equation in slope intercept form through (20,-8) and is perpendicular to 7x - 4y = -5

Answer:

See Explanation

Step-by-step explanation:

First, we calculate the slope of 7x - 4y = -5

7x - 4y = -5

Subtract 7x from both sides

7x-7x - 4y = -5-7x

- 4y = -5-7x

Make y the subject

\frac{- 4y}{-4} = \frac{-5-7x}{-4}

y = \frac{-5-7x}{-4}

y = \frac{5+7x}{4}

y = \frac{5}{4}+\frac{7}{4}x

y = \frac{7}{4}x+\frac{5}{4}

The general format of an equation is:

y= mx + b

Where

m = slope

By comparison:

m = \frac{7}{4}

Solving (1): Parallel

Here, we assume that the line is parallel to the given equation.

And as such, it means that they have the same slope

So, we have:

(x_1,y_1) = (20,-8)

and

m = \frac{7}{4}

The equation is then calculated as:

y - y_1 = m(x - x_1)

This gives:

y - (-8) = \frac{7}{4}(x - 20)

y +8 = \frac{7}{4}(x - 20)

Open bracket

y +8 = \frac{7}{4}x - \frac{7}{4}*20

y +8 = \frac{7}{4}x - 7*5

y +8 = \frac{7}{4}x - 35

Make y the subject

y = \frac{7}{4}x - 35-8

y = \frac{7}{4}x -43

Solving (2): Perpendicular

Here, we assume that the line is perpendicular to the given equation.

And as such, it means that the following relationship exists between their slope:

m_2 = -\frac{1}{m_1}

Where

m_1 =m =\frac{7}{4} -- as calculated above

Substitute 7/4 for m1 in m_2 = -\frac{1}{m_1}

m_2 = -\frac{1}{7/4}

m_2 = -\frac{4}{7}

So, we have:

(x_1,y_1) = (20,-8)

and

m_2 = -\frac{4}{7}

The equation is then calculated as:

y - y_1 = m(x - x_1)

This gives:

y - (-8) = -\frac{4}{7}(x - 20)

y +8 = -\frac{4}{7}(x - 20)

Open bracket

y +8 = -\frac{4}{7}x + \frac{4}{7}*20

y +8 = -\frac{4}{7}x + \frac{80}{7}

Make y the subject

y = -\frac{4}{7}x + \frac{80}{7}-8

y = -\frac{4}{7}x + \frac{80-56}{7}

y = -\frac{4}{7}x + \frac{24}{7}

Take LCM

y = \frac{-4x + 24}{7}

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