Question

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

Answer 1

Answer:

A. Parallel

Step-by-step 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.