find the equation of the straight line passing through the point (4,8) and which is
perpendicular to the line with equation y = -3x + 2.

y = x +

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 3x + 2 ← is in slope- intercept form

with slope m = - 3

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

= - = - = , thus

y = x + c ← is the partial equation

To find c substitute (4, 8) into the partial equation

8 = + c ⇒ c = 8 - =

y = x + ← equation of line

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c

6 equilateral triangles