Answer and Step-by-step explanation: Two lines can be parallel, perpendicular or none of them. The difference is in the slope of a line.
<u>Slope</u> is the change in y over the change in x, or, in other words, it is the steepness of the line.
Two lines are parallel if they don't intersect. So, they have the same slope and different y-intercept. For example:
f(x) = m₁x + b₁
g(x) = m₂x + b₂
Functions f(x) and g(x) are parallel if
m₁ = m₂ and b₁ ≠ b₂
Two lines are perpendicular when they intersect at a 90° angle. For that to happen, the multiplication of the slope of each function must result in -1. For example:
h(x) = m₃x + b₃
j(x) = m₄x + b₄
The functions will be perpendicular if:
If the slopes are not the same or reciprocal, the lines are neither.
Hello!
Let's write some important information contained in the exercise:
• hotdogs: $2.59 (,x,)
,• hamburgers: $5.29 (,y,)
He needs 11 packages. Let's write it:
• x + y = 11
He spent a total of $39.29. We can write it as:
• 2.59x + 5.29y = 39.29
Now, let's solve these two equations as a linear system:
First, let's isolate x in equation A:
Now, we will replace where's x by 11-y in equation B:
As I called the hamburgers as 'y', we know that he bought 4 packages of hamburgers.