Question

A line passes through (2, −1) and (4, 5).

Which answer is the equation of the line?

A. −3x + 5y = 13

B. −3x + y = −7

C. −3x + y = 17

D. −3x + 5y = −13


Which answer is an equation in point-slope form for the given point and slope?

Point: (1, 9); Slope: 5

A. y − 1 = 5 (x + 9)

B. y − 9 = 5 (x − 1)

C. y + 9 = 5 (x−1)

D. y − 9 = 5 (x+1)

Answer 1

the answer to the first question is B
The second question is B

Answer 2

1) Option B is the correct answer.

2) Option B is the correct answer.

Explanation:

1) We have equation of line passing through (x₁,y₁) and (x₂,y₂) given by

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

(x₁,y₁) = (2, −1) and (x₂,y₂) = (4, 5)

Substituting

`y-(-1)=(5-(-1))/(4-2)(x-2)\\\\y+1=3(x-2)\\\\y+1=3x-6\\\\-3x+y=-7`

Option B is the correct answer.

2) Point slope form of line is given by

y-y₁ = m(x-x₁)

(x₁,y₁) = (1, 9) and m = 5

Substituting

y-9 = 5(x-1)

Option B is the correct answer.