Question

Write an equation of the line that passes through the point (–4, 6) with slope –4.

A. y−6=−4(x+4)
B. y+4=−4(x−6)
C. y−6=4(x+4)
D. y+4=4(x−6)

Answer 1

Answer is A

Explanation:

General equation of a line is given by;

`{ \boxed{ \rm{y = mx + c}}}`

• m is gradient
• c is y-intercept.

From the question, m = -4

`{ \rm{y = - 4x + c}}`

For (-4, 6)

`{ \rm{6 = ( - 4 * - 4) + c}} \\ { \rm{6 = 16 + c}} \\ { \rm{c = - 10}}`

Therefore;

`{ \rm{y = - 4x - 10}} \\ { \colorbox{silver}{subtract \: 6 \: from \: both \: sides}} \\ { \rm{y + ( - 6) = ( - 4x - 10) + ( - 6)}} \\ \\ { \rm{y - 6 = - 4x - 16}} \\ \\ { \rm{y - 6 = - 4(x + 4)}}`