Question

(1) What is the equation, in point-slope form, for a line that goes through (8, −4) and has a slope of negative 5/6 (all fractions are negative.)

A) y + 4 = - 5/6 (x + 8)
B) y + 4 = - 5/6 (x - 8)
C) y - 4 = - 5/6 (x + 8) "I think this is the answer but i am not too sure"
D) y - 4 = - 5/6 (x - 8)

(2) What is the equation of a line, in point-slope form, that passes through (−2, −6) and has a slope of 1/3?
A) y - 2 = 1/3 (x - 6)
B) y + 2 = 1/3 (x + 6)
C) y + 6 = 1/3 (x + 2)
D) y - 6 = 1/3 (x - 2)

(3) What is the equation in point-slope form of the line that passes through the points (7, 5) and (−4, −1) ?
A) y + 1 = 6/7 (x + 4)
B) y + 4 = 11/6 (x + 1)
C) y + 1 = 6/11 (x + 4)
D) y - 1 = 6/11 (x - 4)

(4) What is the equation in point-slope form of a line that passes through the points (7, −8) and (−4, 6) ?

A) y − 6 = − 2/3 (x + 4)
B) y + 6 = − 2/3 (x − 4)
C) y + 6 = − 14/11 (x − 4)
D) y − 6 = − 14/11 (x + 4)

Answer 1

its y+1=8/9(x+4)

Answer 2

Formula for point-slope:
`y - y1 = m(x-x1)`
Plug in the values (1):
`y + 4 = -(5)/(6) (x - 8)` {Choice B}
Plug in the values (2):
`y + 6 = (1)/(3)(x+ 2)` {Choice C}
_______________________

[For (3) and (4) we need to solve for slope]

(3)
First, solve for slope.
Formula for slope:
`(y2-y1)/(x2-x1)`
Plug in values:
`(-1-5)/(-4-7) = - (6)/(11)`
Slope:
`- (6)/(11)`
Second, we must plug into point-slope form.
Formula for point-slope:
`y - y1 = m(x-x1)`
Plug in the values:
`y + 1 = - (6)/(11)(x + 4)` {Choice C}


(4)
First, solve for slope.
Formula for slope:
`(y2-y1)/(x2-x1)`
Plug in values:
`(6-(-8))/(-4-7) = - (14)/(11)`
Slope:
`- (14)/(11)`
Second, we must plug into point-slope form.
Formula for point-slope:
`y - y1 = m(x-x1)`
Plug in the values:
`y - 6 = - (14)/(11)(x + 4)` {Choice D}