is the line through points P(-3,-2) and Q(2.3) perpendicular to the line through points R(10,-1) and S(15,-6)? Explain.

We want to see if the two given lines are perpendicular or not.

We will see that yes, the lines are perpendicular.

First, let's define a general linear equation, it is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Two lines are perpendicular if the slope of one is equal to the inverse of the opposite of the slope of the other.

Also, if a line passes through two points (x₁, y₁) and (x₂, y₂) then the slope of the line is given as:

So we can get the slopes of the two given lines, for line PQ we have:

For line RS we have:

So you can see that the slope of line RS is equal to the inverse of the opposite of line PQ.

Then yes, the lines are perpendicular.

If you want to learn more, you can read:

link

Step-by-step explanation:

Line 1 passes through and .

Line 2 is perpendicular to Line 1, and passes through and .

Remember, the condition of perpenticularity between two lines is

Where is the slope of Line 1 and is the slope of Line 2.

Now, the defintion of slope is

Where we are gonna use two points.

Line 1 slope:

Using the condition of perpendicularity

As you can observe, slopes are opposite number, they aren't equal. Also, as we said before, the condition of perpendicularity is , that is, their slopes have a product of -1.

Therefore, the right choice is C.

Cost of 7 gallons=$24.50

Cost of 1 gallon=24.50/7=3.5

Cost of 15 gallons=15*3.5=52.5

Cost of 15 gallons will be $52.5

The answer is in the image