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# Lines, matrices, and supply and demand

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1) Best Rentals charges a daily fee plus a mileage fee for renting its cars. Barney was charged \$ 147 for 3 days and 300 miles, while Mary was charged \$ 268 for 5 days and 600 miles. What does Best Rental charge per day and per mile?
Write an equation for the line. Use slope-intercept form, if possible.
2) Through ( 5, -6) and ( 0, -8)
Use the echelon method to solve the system of two equations in two unknowns.
3) 5x - 7y = 8
3x - 4y = 5
Write the augmented matrix for the system. Do not solve.
4) -2x + 6y = 40
2x + 2y = 8
Find the slope of the line passing through the given pair of points.
5) ( 3, 2) and ( 3, 9)
Use the echelon method to solve the system of three equations in three unknowns.
6) x + y + z = 2
x - y + 5z = 0
4x + y + z = 14
Find the slope of the line.
7) A line parallel to 4y - 5x = -7
Use the echelon method to solve the system.
8) x/2 + y/2 = 0
x - y = -12
Solve the problem.
9) Let the supply and demand functions for a certain model of electric pencil sharpener be given by
p = S(q) = 2/3q and p = D(q) = 15 - 4/3q
where p is the price in dollars and q is the quantity of pencil sharpeners (in hundreds). Graph these functions on the same axes (graph the supply function as a dashed line and the demand function as a solid line). Also, find the equilibrium quantity and the equilibrium price.
Find the slope of the line.
10) A line parallel to -4x = 5y + 11
Use the echelon method to solve the system of two equations in two unknowns.
11) x - 2y = -2
6x - 3y = -30
Provide an appropriate response.
12) Find k so that the line through (3, k) and (1, -2) is parallel to 5x - 3y= -2. Find k so that the line is perpendicular to 3x + 2y = 6
Write an equation for the line. Use slope-intercept form, if possible.
13) Through ( 4, 0), m = -1
Write the augmented matrix for the system. Do not solve.
14) 4x - 2y = 14
-2y = -2
Find the slope of the line passing through the given pair of points.
15) ( 5, 4) and ( 2, 2)
Use the Gauss-Jordan method to solve the system of equations.
16) 3x + 3y = -6
2x + 8y = 14
Write an equation for the line. Use slope-intercept form, if possible.
17) Through ( 3, 5), m = - 5/9
Find the slope of the line.
18) 5x + 2y = 16
Use the echelon method to solve the system of two equations in two unknowns.
19) x + 3y = 9
-7x + 4y = 12
Find the slope of the line passing through the given pair of points.
20) ( 6, -4) and ( -7, 1)