Question

I need help understanding this ASAP plz, I have a quiz over this next week!!!!

Answer 1

Explanation:

With any two points, you can find the line between them with:

`y = mx + b\\where\\m = (y_2-y_1)/(x_2-x_1)`

#1:

(-1, 1) -> (1, 3)
`m = (3-1)/(1-(-1)) = 1, 3 = 1(1) + b, b = 2, y = x + 2`

(3, 4) -> (0, 2)
`m = (4-2)/(3-0) = (2)/(3), 2 = (2)/(3)(0) + b, y = (2)/(3)(x)+2`

(0, 1) -> (3, 3)
`m = (3-1)/(3-0) = (2)/(3), 1 = 2/3(0) + b, y = (2)/(3)(x) + 1`

Lines b and c are parallel because they have the same slopes

#2 is a bit easier

a: 2y = x + 12,
`y = (1)/(2)(x) + 6`

b:2y - x = 5,
`y = (1)/(2)(x) + (5)/(2)`

c: 2y + x = 4,
`y = (-1)/(2)(x) + 2`

Since lines a and b have the same slope, they are parallel

#3:

(1, 3), y = 2x - 5

We have to find a line with a slope of 2 that passes through the two points

`y = 2x + b\\3 = 2(1) + b\\b = 1\\\\y = 2x + 1`

#4:

(-2, 1) , y = -4x + 3

We have to find a line with a slope of-4 that passes through the line

`y = -4x + b\\1 = -4(-2) + b\\1 = 8+ b\\b = -7\\y = -4x - 7`

#5:

(-2, 3) (1, -1),
`m = (3-(-1))/(-2-1) = (-4)/(3), 3 = (8)/(3) + b, b = (1)/(3), y = (-4x)/(3) + (1)/(3)`

(-3, 1) (1, 4),
`m = (4-1)/(1-(-3)) =(3)/(4), 4 = (3(1))/(4) + b, y = (3)/(4)(x) + (13)/(4)`

(0, 2) (3, -2)
`m = (2-(-2))/(0-3) = (-4)/(3) , 2 = b, y = (-4)/(3)(x) + 2`

Since lines c and b have negative reciprocal slopes, they are perpendicular

#6:

a: y = -4x + 7

b: x = 4y + 2,
`y = (x)/(4) - (1)/(2)`

c: -4y + x = 3,
`y = (x)/(4) - (3)/(4)`

since lines a and c have negative reciprocal slopes, they are perpendicular