Question

What is the equation of a line parallel to -x+3y=-6 that passes through 9,-1

Answer 1

`{ \tt{ - x + 3y = - 6}} \\ { \tt{3y = x - 6}} \\ { \tt{y = (1)/(3)x - 2 }}`

• For parallel line, their gradients are the same:

→ m = ⅓

• From general equation of a line;

`→ \: { \tt{y = mx + c}} \\`

• For the point (9, -1):

`→ \: { \tt{ - 1 = (9 * (1)/(3) ) + c}} \\ \\→ \: { \tt{ - 1 = 3 + c}} \\ \\ → \: { \tt{c = - 4}}`

therefore:

`→ \: { \boxed{ \tt{y = (1)/(3)x - 4 }}}`