Write an equation for the line that is parallel to the given line and passes through the given point y = 5x + 10; (2, 14) a) y = 1/5x + 4 b) y = -1/5x - 4 c) y = 5x - 68 d) y = 5x + 4

D

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 = 5x + 10 is in this form with slope m = 5

• Parallel lines have equal slopes, hence

y = 5x + c ← is the partial equation

to find c substitute (2, 14) into the partial equation

14 = 10 + c ⇒ c = 14 - 10 = 4

y = 5x + 4 ← equation of parallel line → D

(-5,-28)

i graphed to on desmos.

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