Question

Please help me with my algebra homework (Attachment)

Answer 1

Option D

Explanation:

→ Find the gradient of the parallel line

`y=-(2)/(3) x+c`

→ Substitute in the coordinates as x and y values to find c

`5=-(2)/(3) *-4+c`

→ Simplify

`5=(8)/(3) +c`

→ Minus
`(8)/(3)` from both sides to find c

`c = (7)/(3)`

→ Expand out all options and then see which one contains all the numbers above

Option D

Answer 2

D.

Explanation:

To see if a line is parallel to y = -(2/3)x + 8 you need to check if the coefficients at y and x are of the same ratio. This immediately removes answers A and C, because of the wrong sign at x compared to y.

What's left is to see which of the answers B and D passes through (4, -5) by inputting x = 4 and y = -5

B.

left = -5 - 5 = -10

right = -(2/3)(4 + 4) = -16/3

So it's D. Let's verify:

D.

left = -5 + 5 = 0

right = -(2/3)(4 - 4) = 0

Checks out.