Mathhhhhhhhh :/

Question

a) For what value of a are the graphs of y = 1/3x + 10 and y = ax -15 parallel?

b) For what value of a are the graphs of y = 1/3x + 10 and y = ax -15 perpendicular?

Answer 1

a) Two lines are parallel if their slopes are equal, m₁ = m_2,

The two equations are written in slope intercept form y= mx + c, where m is the slope of the line

For the first line y = 1/3x + 10, m₁=1/3

for the second line y = ax -15, m₂=a

so for the two lines to be parallel m₁ and m₂ has to be equal ,

1/3 = a, a=1/3

b) Two lines are perpendicular if the multiplications of their slopes is -1, m₁ * m₂ = -1

1/3* a = -1 , multiplying both sides by 3 we get,

a = -3

Answer 2

Parallel graphs have the same slope, otherwise, they would meet up at some point eventually, so the a in your first example must be 3.

If graph a has slope a and graph b is perpendicular to graph a, for slightly more complicated reasons, graph b has the slope -1/a. So in this case, since graph a has slope 1/3, graph b has slope -1/(1/3) = -3, so a = -3 in your second example.