Line t passes through (4, 5) and is perpendicular to the line shown on the coordinate grid. a coordinate plane with a line passing through two points at 0 comma 3 and 6 comma 2 what is the equation of line t in standard form?
a. x + 6y = 114
b.−6x − y = 19
c .x − 6y = −114
d. 6x − y = 19

option d. 6x − y = 19

step-by-step explanation:

step 1

find the slope of the given line that passes through the points (0,3) and (6,2)

m=(2-3)/(6-0)

m=-1/6

step 2

find the slope of the line t

we know that

if two lines are perpendicular, then the product of their slopes is equal to -1

m1*m2=-1

we have

m1=-1/6

substitute

(-1/6)*m2=-1

m2=6

step 3

find the equation of the line t

the equation of the line into point slope form is equal to

y-y1=m(x-x1)

we have

m=6

point (4,5)

substitute

y-5=6(x-4)

y=6x-24+5

y=6x-19

6x-y=19