Part One: Graphing Linear Equations

Honors 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 Subtract 7x from each side

-y = -7x – 7

y = 7x + 7 Multiply or divide each term by -1

2. Pick 3 numbers for x and plug them into the equation to find y.

7(1) + 7 = 14

7(0) + 7 = 7

7(-1) + 7 = 0

3. Plot the points on a graph then draw the line.

X Y

1 14

0 7

-1 0


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 5(0) – 3y = 10

5x = 10 -3y = 10

x = 2 y = -10/3

x-intercept (2, 0) y-intercept (0, - 3 1/3)

Graph the two intercept points and draw the line.


Graph the following equations using the x and y intercepts. Remember that you can find the x-

intercept 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: my y

x x

2 1

2 1

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)


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 y-

intercept.

12. 6x – 2y = -16 13. -2x + 5y = 15


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

Part Two: Writing Equations of Lines


Write an equation of each line in Standard Form with the given information.

1. m = -6/5 b = -2 2. m = ½ b = 3

3. (7, -2) and m = 8/7 4. (1, -1) (4, 5)

5. Write and equation of a line in slope-intercept form that is parallel to 2x – y = 7 and contains

the point (3, 4). (Remember that parallel lines have the same slope.)

6. Write an equation of a line in slope-intercept form parallel to x – 5y = 12 and through the

point (-10, 4). (Remember that perpendicular lines have inverse and opposite slopes.)


7. Write and equation of a line in slope-intercept form perpendicular to x – 6y = 2 and through

the point (2, 4).

8. Write and equation of a line in slope-intercept form perpendicular to 3x + 2y = -7 and through

the point (6, -3).

9. Write and equation of a line through (3, 5) and m = 2/3 in standard form.

10. Write and equation of a line through (2, 1) and (4, -1) in standard form.

11. Find an equation for the line through (2, 7) and (3, 2) in slope intercept form.

12. Find and equation for the line with m = 2/3 and containing (3, -1) in slope intercept form.


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. xy

4 - 14y

2

3. 18x3y

2 + 42x

2y

3 4. 3x

2 – 9x + 12y

5. 10x2 – 30xy + 45y

2 6. 36x

2 + 18x

3 – 6x + 12x

4

Example: Factoring a trinomial with an x2 leading.


Factor the following completely; if the polynomial is prime (not factorable), say so

7. x2 – 9x + 8 8. x

2 – 2x – 35

9. x2 – 9xy + 12y

2 10. x

2 – 6x -27

11. x2 – 16x + 64 12. 21 – 4x – x

2

Example: Factoring a trinomial with a 3x2 leading.

Example: Difference of squares.


Factor the following completely; if the polynomial is prime (not factorable), say so.

13. 3x2 + 4x + 1 14. 4x

2 – 17x + 15

15. 4x2 – 25 16. 3x

2 -7x – 6

17. 9x2 – 64y

2 18. 2x

2 + 4x + 6

19. 4x2 + 8x + 3 20. 6x

2 + 7x – 10


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.



3. 4. 5.

MULTIPLYING/DISTRIBUTING RADICALS To multiply square roots, you multiply the coefficients together and the radicands together.

Always simplify your final answer.

Distribute 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.


9. 10.

Radical Mixed Practice: Simplify each expression.

11. 12. 13.

14. 15. 16.

17. 18.

19. 20.


Part Five: Solving Systems of Equations

Solve each system of equations by GRAPHING.

1. 2.


Solve each system of equations

by SUBSTITUTION.

3. 4.

Solve each system of equations

by ELIMINATION.

You may have to multiply both equations by something to make x or y cancel.

5. 6.

Documents

Part One: Graphing Linear Equations