Question

Consider the equation 5y = 2x +4. Select all the equations that are perpendicular to the given equation.

Answer 1

Answer:

see the explanation

Step-by-step explanation:

we have

$5y=2x+4$

Solve for y

$y=\frac{2}{5}x+\frac{4}{5}$

This is the equation of  the line in slope intercept form

The slope m of the given equation is

$m=\frac{2}{5}$

we know that

If two lines are perpendicular,, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

so

Find the slope of the line perpendicular to the given line

$m1*m2=-1$

we have

$m1=\frac{2}{5}$

substitute

$(\frac{2}{5})*m2=-1$

$m2=-\frac{5}{2}=-2.5$

therefore

All equations of the line having as slope $m=-2.5$ will be perpendicular to the given line.