Question

(-3,1) perpendicular to y=2/5x-4

Answer 1

(-3, 1)             y = 2/5x - 4 
 x₁  y₁              slope (m) = 2/5x

Since the equation we are looking for is perpendicular to y = 2/5x - 4, we need to find the opposite reciprocal slope. We have to flip the slope upside down and turn it negative.

2/5 ⇒ 5/2 ⇒ -5/2

So far, we have the equation y = -5/2.

Now, we need to find the y intercept by plugging in the given point into point slope form, which is...

y - y₁ = m(x - x₁) 

The subscripts in the y and x are just the x and y in (-3,1). They are just placeholders, not exponents.

y - 1 = -5/2(x + 3)
 y - 1 = -5/2x - 15/2
   + 1               +     1
------------------------------
 y = -5/2x - 13/2 ⇒ final equation

Answer 2

The equation of a line passing through the point $(-3,1)$ and perpendicular to the line $y=\frac{2}{5}x-4$ is $y=-\frac{5}{2}x-\frac{13}{2}$.

The product of the slopes of two perpendicular lines is $-1$.

$y=\frac{2}{5}x-4$, slope $= \frac{2}{5}$

So, slope of a line perpendicular to this line is $-\frac{1}{\frac{2}{5}}= -\frac{5}{2}.$

And, this line passes through the point $(-3,1)$.

Equation of a line that passes through a point $(x_1, y_1)$ and slope $m$ is:

$(y-y_1)=m(x-x_1)$

Here, $x_1=-3, y_1=1, m=-\frac{5}{2}$.

$(y-1)=-\frac{5}{2}(x+3)$

$(y-1)=-\frac{5}{2}x-\frac{5}{2} \times 3$

$(y-1)=-\frac{5}{2}x-\frac{15}{2}$

$y=-\frac{5}{2}x-\frac{15}{2}+1$

$y=-\frac{5}{2}x-\frac{13}{2}$

Learn more here:

https://brainly.com/question/45942?referrer=searchResults