REVIEW FOR LINEAR FUNTIONS TEST define and identify: coordinate plane, linear equation, origin, parallel lines, perpendicular lines, quadrant,

axes, x-axis, y-axis, ordered pair, x-coordinate, y-coordinate, x-intercept, y-intercept

graph ordered pairs and linear equations

graph and identify special linear equations, which include horizontal lines (y = a), vertical lines (x = b), and

y = x and y = -x

state and identify the slope and y-intercept of a graph of a linear equation

state & identify the slope (m) & y-intercept (b) from a linear equation in slope-intercept form: y = mx + b

transform a linear equation into slope-intercept form

write a linear equation in slope-intercept form given the graph

determine if an ordered pair is a solution for a linear equation

write a linear equation: (1) given the slope and y-intercept, (2) given the slope and a point, (3) given two

points, (4) given information about a parallel line, (5) given information about a perpendicular line

solve systems of linear equations graphically

solve systems of linear equations algebraically, using the addition method and substitution method

solve word problems related to linear systems

College Algebra: Functions and Models Name:____________________________________

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Review- Linear Functions and Systems TestDate:_____________________________________

1. State the equation of x –axis: 2. State the equation of y-axis: ______

3. What is the slope-intercept form of a linear equation?

4. Find the slope and y-intercept of each of the following equations:

a. y = -x b. x – y =7 c. x = - 2

d. 2y = 5x – 3

e. 2x + 7y = 49 f. y = 4

Graph the following linear equations:

(5) y = 2x – 1 (6) y = -½x + 2

(7) y = 5 (8) x = -32

(9) 3x – 4y = -4

(10) Is the point (-1, 3) on the line 2x + y = 7? Justify your answer algebraically.

(11) The point (3, k) is on the line whose equation is -3x – 2y = 5. Find the value of k.

(12) Write an equation of a line whose slope is -⅝ and y-intercept is -7.

(13) Write an equation of a line whose slope is -⅓ and passes through the point (-6, 0).

(14) Write an equation of a line that passes through the points (3, 4) and (-3, 0).

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(15) Write an equation of a line that is parallel to the line 2y – 4x = 9 and passes through the point (-2, 1).

(16) Write an equation of a line that is perpendicular to the line 3y + 2x = 6 and passes through the point (2, 4).

Solve for the two variables. Use the Addition/Elimination Method:

(17) 5a + 3b = 174a – 5b = 21

(18) 7x = 5 – 2y3y = 16 – 2x

(19) x – 2y = -4x – y = -4

(20) 5x – 2y = 222y + x = 2

Solve for the two variables. Use the Substitution Method:

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x

y

x

y

x

y

(21) 4x + 3y = 27y = 2x – 1

(22) 3x – 4y = 26x + 2y = 2

(23) 3m – 2n = 11m + 2n = 9

(24) a – 2b = -22a – b = 5

For each system of equations, graph the system, solve the system, and check your solution.

(25) 2y + x = 1y + 2x = 5

(26) y = -xy = 2x – 6

(27) x + y = 2

5

x

y

2y – x = 10

(28) y = x – 4 3y = x – 6

(29) The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is collected. How many children and how many adults attended?

(30) A landscaping company placed two orders with a nursery. The first order was for 13 bushes and 4 trees, and totaled $487. The second order was for 6 bushes and 2 trees, and totalled $232. The bills do not list the per-item price. What were the costs of one bush and of one tree?

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