Answer:
A. Parallel
Step-by-step explanation:
Given: Equations [tex]\text{y}=3\text{x}+5[/tex] and [tex]\text{-y}=-3\text{x}-13[/tex]
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 = [tex]\text{y}=3\text{x}+5[/tex]
Equation of Line 2 = [tex]\text{-y}=-3\text{x}-13[/tex]
We know that,
standard equation of line is,
[tex]\text{y}=\text{m}\text{x}+c[/tex]
writing equation of lines in standard form
Line 1, [tex]\text{y}=3\text{x}+5[/tex]
Line 2, [tex]\text{y}=3\text{x}+13[/tex]
Comparing with standard equations we find out that
Slope of Line 1= [tex]3[/tex]
Slope of Line 2= [tex]3[/tex]
therefore graphs of both equations is parallel, now we have to check if they are coincidental
intercept [tex]\text{c}[/tex] of line 1 = [tex]5[/tex]
intercept [tex]\text{c}[/tex] of line 2 = [tex]13[/tex]
intercept [tex]\text{c}[/tex] of line 1 ≠ intercept [tex]\text{c}[/tex] of line 2
Graphs are not coincidental
Therefore Option A is correct Graphs of both equations are parallel.
