Linear Equations and Functions

We want a line that goes through the point (2, -7) and is perpendicular to 5x + 2y = 18

We will first find the slope of our new line, then we will find the intercept
• Our line is perpendicular to 5x + 2y = 18, let's put this in slope intercept form
• 2y = 5x - 18
• y = (-5/2)x - 18, the slope of this line is -5/2
• Our new line is perpendicular to the original line so its slope is m = -1/(-5/2) = 2/5
• We can now write y = (2/5) x + b
• To find b we must use the point (2, -7) which satisifies our new equation
• -7 = 2(2/5) + b
• -7 = 4/5 + b
• b = -7 - 4/5 = -35/5 - 4/5 (we got -35/5 by multiplying - 7 by 5/5, doesn't change value, gives us LCD)
• b = -35/5 - 4/5 = -39/5
• Our equation is y = (2/5) x - 39/5

There is a $30 fee to rent a chain saw, plus $6 per day. Let x represent the number of days the saw is rented and y represent the charge to the user in dollars. If the total charge is $138, for how many days is the saw rented.

Heading to section asks us to
• (a) write an equation in y = mx + b form,
• (b)find and interpret the ordered pair associated with x = 5
• (c)answer the question

Let's start with writing the equation. We want our equation in y = mx + b format
• The fixed charge is $30. This is the value of b, we pay it when x = 0.
• The variable cost is $6 per day. This is the value of m, the cost per day.
• Our equation is cost = 6*days plus fixed charge or y = 6x + 30. This is the answer to (a)
• When x = 5 we have y = 6*5 + 30 = 30 + 30 = $60. This is the charge for 5 days of saw rental. Answer to (b)
• If the total cost is $138 we have 138 = 6x + 30
• 138 - 30 = 6x + 30 - 30 (we have subtracted 30 from both sides of the equation)
• 108 = 6x
• x = 108/6 = 18, we have used the saw for 18 days