Question

A line contains the piont (4,5) and is perpendicular to a line with a slope of -2/3. Write an equarion of the line satisfying the given conditions. Write the answer in slope-intercept form

Answer 1

Answer:

$y=\frac{3}{2}x-3.5$ or, preferably, $y=\frac{3}{2}x-\frac{7}{2}$

Step-by-step explanation:

First is to find the perpendicular slope. In this case, you swap the numerator and denominator and then multiply that fraction by -1.

In this case, -2/3's inverse slope is 3/2.

Now, the initial y=3/2 passes through 7.5,5

So, you must subtract 3.5 from that to make it pass through 4,5.

In this way, you get the answer in slope-intercept form.

Answer 2

Answer:

y = $\frac{3}{2}$ x - 1

Step-by-step explanation:

Given a line with slope m then the slope of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{-\frac{2}{3} }$ = $\frac{3}{2}$ , then

y = $\frac{3}{2}$ + c ← partial equation in slope- intercept form

To find c substitute (4, 5) into the partial equation

5 = 6 + c ⇒ c = 5 - 6 = - 1

y = $\frac{3}{2}$ x - 1 ← equation of line