Respuesta :
Answer:
15. The lines are perpendicular.
16. The lines are neither perpendicular nor parallel.
Step-by-step explanation:
15. The given lines are
Y=-3x+7 & -2x+6y=3 or, 6y = 3 + 2x or, [tex]y = 0.5 + \frac{x}{3}[/tex].
The slope of the first line is -3 and the slope of the second line is [tex]\frac{1}{3}[/tex] [Comparing with the standard form of equation of straight line y = mx + c, where m is the slope of the straight line].
Two straight lines will said to be perpendicular to each other, if the product of its slopes will be equal to -1.
Since, [tex]-3 \times \frac{1}{3} = -1[/tex], the equations are perpendicular with respect to each other.
16. The lines are [tex]y = -\frac{x}{5} + 6[/tex] and -2x + 10y = 5 or, 10y = 5 + 2x or, [tex]y = 0.5 + \frac{x}{5}[/tex].
As per the question number 15, it is clear that these equations are not perpendicular.
Here, the slope of the first one is [tex]\frac{-1}{5}[/tex] and the slope of the second one is [tex]\frac{1}{5}[/tex].
The values are same with different sign. Hence, these equations are not parallel too.
