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

Sagot :

MrRoyal

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 [tex]7x - 4y = -5[/tex]

[tex]7x - 4y = -5[/tex]

Subtract 7x from both sides

[tex]7x-7x - 4y = -5-7x[/tex]

[tex]- 4y = -5-7x[/tex]

Make y the subject

[tex]\frac{- 4y}{-4} = \frac{-5-7x}{-4}[/tex]

[tex]y = \frac{-5-7x}{-4}[/tex]

[tex]y = \frac{5+7x}{4}[/tex]

[tex]y = \frac{5}{4}+\frac{7}{4}x[/tex]

[tex]y = \frac{7}{4}x+\frac{5}{4}[/tex]

The general format of an equation is:

[tex]y= mx + b[/tex]

Where

[tex]m = slope[/tex]

By comparison:

[tex]m = \frac{7}{4}[/tex]

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:

[tex](x_1,y_1) = (20,-8)[/tex]

and

[tex]m = \frac{7}{4}[/tex]

The equation is then calculated as:

[tex]y - y_1 = m(x - x_1)[/tex]

This gives:

[tex]y - (-8) = \frac{7}{4}(x - 20)[/tex]

[tex]y +8 = \frac{7}{4}(x - 20)[/tex]

Open bracket

[tex]y +8 = \frac{7}{4}x - \frac{7}{4}*20[/tex]

[tex]y +8 = \frac{7}{4}x - 7*5[/tex]

[tex]y +8 = \frac{7}{4}x - 35[/tex]

Make y the subject

[tex]y = \frac{7}{4}x - 35-8[/tex]

[tex]y = \frac{7}{4}x -43[/tex]

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:

[tex]m_2 = -\frac{1}{m_1}[/tex]

Where

[tex]m_1 =m =\frac{7}{4}[/tex] -- as calculated above

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

[tex]m_2 = -\frac{1}{7/4}[/tex]

[tex]m_2 = -\frac{4}{7}[/tex]

So, we have:

[tex](x_1,y_1) = (20,-8)[/tex]

and

[tex]m_2 = -\frac{4}{7}[/tex]

The equation is then calculated as:

[tex]y - y_1 = m(x - x_1)[/tex]

This gives:

[tex]y - (-8) = -\frac{4}{7}(x - 20)[/tex]

[tex]y +8 = -\frac{4}{7}(x - 20)[/tex]

Open bracket

[tex]y +8 = -\frac{4}{7}x + \frac{4}{7}*20[/tex]

[tex]y +8 = -\frac{4}{7}x + \frac{80}{7}[/tex]

Make y the subject

[tex]y = -\frac{4}{7}x + \frac{80}{7}-8[/tex]

[tex]y = -\frac{4}{7}x + \frac{80-56}{7}[/tex]

[tex]y = -\frac{4}{7}x + \frac{24}{7}[/tex]

Take LCM

[tex]y = \frac{-4x + 24}{7}[/tex]

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