Question

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

Answer 1

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

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