Question

Please help 30 points!!'

Answer 1

Answer:

The equation of line perpendicular to given line passing through (-15,-4) is:

$y = -\frac{4}{3}x-24$

Step-by-step explanation:

Given equation is:

$3x-4y = 9$

The given equation is in standard form. We have to convert it into slope intercept form first.

The slope intercept form is:

$y = mx+b$

So,

$3x-4y=9\\3x-9 = 4y\\4y = 3x-9\\\frac{4y}{4} = \frac{3x-9}{4}\\y = \frac{3}{4}x - \frac{9}{4}$

The co-efficient of x is the slope of the line.

m = 3/4

The product of slopes of two perpendicular lines is: -1

Let m1 be the slope of line perpendicular to given line then

$m.m_1 =-1\\\frac{3}{4} . m_1 = -1\\m_1 = -1 * \frac{4}{3} \\m_1 = -\frac{4}{3}$

Putting in slope-intercept form

$y = m_1x+b\\y = -\frac{4}{3}x+b$

To find the value of b, putting (-15,-4) in equation

$-4 = -\frac{4}{3}(-15) +b\\-4 = 20+b\\-4-20 = b\\b = -24$

The equation will be:

$y = -\frac{4}{3}x-24$

Hence,

The equation of line perpendicular to given line passing through (-15,-4) is:

$y = -\frac{4}{3}x-24$