Download Review: Equations of lines

Algebra 2 Summer Math
Name:
Part One: Graphing Linear Equations
Graph each point and label it with the appropriate letter. On the line next to the point write the
quadrant or axis where the point lies. (I, II, III, IV, x-axis, y-axis)
1. A (2, -1) _____________
2. B (3, 0) ______________
3. C (-4, -2) ____________
4. D (0, 2) _____________
5. E (-5, 4) _____________
Graph each line using a table of values.
1. Solve for y
7x – y = -7
-7x
-7x
-y = -7x – 7
y = 7x + 7
Subtract 7x from each side
Multiply or divide each term by -1
2. Pick 3 numbers for x and plug them into the equation to find y.
X
Y
1
0
-1
14
7
0
7(1) + 7 = 14
7(0) + 7 = 7
7(-1) + 7 = 0
3. Plot the points on a graph then draw the line.
Algebra 2 Summer Math
Name:
Graph each line by making a table and plotting the points. Be sure to solve the equation for y
first. You should have three points for each table of values.
6. 3y + 12x = -3
X
Y
7. x + 2y = -4
X
Y
Finding the x and y intercepts.
To find the x intercept make y = 0. To find the y intercept make x = 0.
Find the x and y intercepts of the equation.
5x – 3y = 10
x-intercept
(y = 0)
y-intercept
(x = 0)
5x – 3(0) = 10
5x = 10
x=2
5(0) – 3y = 10
-3y = 10
y = -10/3
x-intercept (2, 0)
y-intercept (0, - 3 1/3)
Graph the two intercept points and draw the line.
Algebra 2 Summer Math
Name:
Graph the following equations using the x and y intercepts. Remember that you can find the xintercept by substituting 0 in for y and that you can find the y-intercept by substituting 0 in for x.
8. 4x + 2y = 16
9. 12x + 9y = 3
Slope: Rise over Run
Slope Formula: m 
y2  y1
x2  x1
Find the slope of the line through the points using the slope formula.
10. (-4, 6) and (-3, 2)
11. (-10, -7) and (1, -2)
Algebra 2 Summer Math
Name:
Graph each of the following using only the slope and y-intercept. Solve the equation for y to
change it into slope-intercept (y = mx + b) form. Remember that m is the slope and b is the yintercept.
12. 6x – 2y = -16
13. -2x + 5y = 15
Algebra 2 Summer Math
Name:
Graph each of the following special case lines.
Special Cases
The slope of a horizontal line is 0. The equation of a horizontal line is y = c.
The slope of a vertical line is undefined. The equation of a vertical line is x = c.
14. x = 3
15. y = -2
Algebra 2 Summer Math
Name:
Given the slope of the line, determine the slope of a line parallel and perpendicular.
Slope of the line
16.
17.
18.
19.
Slope of a line parallel
m = 2/3
m = -5
m=0
m = -1
Part Two: Solving Equations
Slope of a line perpendicular
Algebra 2 Summer Math
Name:
Solve each equation and check your solution.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
Algebra 2 Summer Math
Name:
Part Three: Factoring
Factoring is the opposite of multiplication (distribution) and FOILing. You should always start
by factoring out the Greatest Common Factor (GCF). It is the biggest number/letter that is a
multiple of all the terms.
Example: Factor by the GCF
Factor the following questions using the GCF:
1. 3z2 + 6z
2. xy4 - 14y2
3. 18x3y2 + 42x2y3
4. 3x2 – 9x + 12y
5. 10x2 – 30xy + 45y2
6. 36x2 + 18x3 – 6x + 12x4
Example: Factoring a trinomial with an x2 leading.
Algebra 2 Summer Math
Name:
Factor the following completely; if the polynomial is prime (not factorable), say so
7. x2 – 9x + 8
8. x2 – 2x – 35
9. x2 – 9xy + 12y2
10. x2 – 6x -27
11. x2 – 16x + 64
12. 21 – 4x – x2
Example: Factoring a trinomial with a 3x2 leading.
Example: Difference of squares.
Algebra 2 Summer Math
Name:
Factor the following completely; if the polynomial is prime (not factorable), say so.
13. 3x2 + 4x + 1
14. 4x2 – 17x + 15
15. 4x2 – 25
16. 3x2 -7x – 6
17. 9x2 – 64y2
18. 2x2 + 4x + 6
19. 4x2 + 8x + 3
20. 6x2 + 7x – 10
Algebra 2 Summer Math
Name:
Part Four: Radicals
Simplifying Radicals and Radical Expressions
SIMPLIFYING RADICALS
(perfect squares: 1, 4, 9, 16, 25, 36, 49…)
Simplify each expression.
2.
ADDING AND SUBTRACTING RADICALS
To add or subtract square roots, they have to have the same radicand (number under the radical).
You may have to simplify the radicals first.
Simplify each expression.
3.
4.
5.
Algebra 2 Summer Math
Name:
MULTIPLYING/DISTRIBUTING RADICALS
To multiply square roots, you multiply the coefficients together and the radicands together.
Always simplify your final answer.
Distribute each expression.
Simplify each expression.
6.
7.
8.
DIVIDING BY RADICALS/RATIONALIZING THE DENOMINATOR
In order for a fraction to be simplified, the expression in the denominator cannot have a radical in
it. Rationalizing the denominator is a procedure for making that happen.
Simplify each expression.
9.
10.
Algebra 2 Summer Math
Name:
Radical Mixed Practice: Simplify each expression.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.