Question

Determine whether the graphs of y = 3x + 5 and -y = -3x - 13 are parallel, perpendicular, coincident, or none of these.

a. Parallel c. Perpendicular b. Coincident d. None of These

Please select the best answer from the choices provided
A
B
C
D

Answer 1

The answer is A, parallel.

Answer 2

A. Parallel

Explanation:

Given: Equations
`\text{y}=3\text{x}+5` and
`\text{-y}=-3\text{x}-13`

To Find: whether the graphs of y = 3x + 5 and -y = -3x - 13 are parallel, perpendicular, coincident, or none of these.

Solution:

As Equations are linear

Equation of Line 1 =
`\text{y}=3\text{x}+5`

Equation of Line 2 =
`\text{-y}=-3\text{x}-13`

We know that,

standard equation of line is,

`\text{y}=\text{m}\text{x}+c`

writing equation of lines in standard form

Line 1,
`\text{y}=3\text{x}+5`

Line 2,
`\text{y}=3\text{x}+13`

Comparing with standard equations we find out that

Slope of Line 1=
`3`

Slope of Line 2=
`3`

therefore graphs of both equations is parallel, now we have to check if they are coincidental

intercept
`\text{c}` of line 1 =
`5`

intercept
`\text{c}` of line 2 =
`13`

intercept
`\text{c}` of line 1 ≠ intercept
`\text{c}` of line 2

Graphs are not coincidental

Therefore Option A is correct Graphs of both equations are parallel.