Download Algebra 2/Trigonometry Honors Name: Assignment:

Algebra 2/Trigonometry Honors
Name:
Assignment: 3.1-3.3
Mods:
Date:
Pay special attention to anything I have starred.  These are strategies that I need you to focus on.
3.1 Graphing Linear Equations

Standard/General Form: Ax + By = C where A, B, & C are integral coefficients (not fractions,
decimals, etc.)

Slope-Intercept Form: y = mx + b (where m = slope and b = y-intercept)

 Point-Slope Form: y – y1 = m(x – x1) where m = slope and (x1, y1) is a point on the line.
1) Use point-slope form and leave your answer in standard form. Find the line passing through the
points (-4, 8) and (5, 12)
2) Use slope-intercept form and leave your answer in standard form. Find the line perpendicular to
-4x + 5y = 12 and passing through the point (8, -6)
3) Use point-slope form and leave your answer in standard form. Find the line with a slope of

2
and passing through the point (12, -5).
7
4) Find the linear function, h(x), if h(3) = 10 and h(5) = 7.
5) Kath sells popcorn to raise money for the school French club. A small box sells for $0.30 and a large
box sells for $0.50.
a) How much money will Kathy collect if she sells 12 small boxes and 15 large boxes?
b) Write an expression for the total amount of money that Kathy would collect if she sold x small
boxes of popcorn and 3 more large boxes than small boxes.
c) If Kathy sold 3 more large boxes than small boxes and collected $25.50, how many boxes of
popcorn did Kathy sell all together?
6) Write an equation of a line that has a slope of 0 and passes through the point (-5, 0).
7) In the diagram, AD is perpendicular to B C . Find the value of k.
8)
9) Let h(x) = 3x – 10. Find all the values of a for which h(a) + h(a + 1) = h(a + 2)
3.2 Systems of Linear Equations

Solving using 2 strategies ---- Graphing, Substitution, and Elimination (be comfortable with
all)
10) Use the diagram to solve for x and y.
11) Find x and y if the perimeter of rectangle A is 26 and the perimeter of rectangle B is 24.
12) Solve for (x, y) using elimination. Leave answers as simplified improper fractions or mixed numbers.
No decimals
 4 x  6 y  7

 3 x  5 y  12
13) Solve for (x, y) using substitution. Leave answers as simplified improper fractions or mixed
numbers. No decimals.
 x  3 y  32

 3 x  y  1
14) If the two equations x + y =10 and y = mx + 5 are graphed on the same coordinate plane and if m is
3
1
1 3
randomly chosen from {2,  , 1,  , 0, ,1, , 2} , what is the probability that the two line will intersect
2
2
2 2
in the first quadrant?
15) Find the value of k for which the slope of the line through (-2, k) and (5, 3k – 4) is 8.
16) If x + 2y = 12 and 3x – 7y = 16, what is the value of 4x – 5y?
17) Refer to the graph. Estimate the coordinates of the point where the lines intersect; then find the
exact coordinates of the point.
18) A chemistry student needs 40 ml of a 14% acid solution. She had two solutions, A and B, to mix
together to form the 40 ml acid solution. Acid solution A is 10% acid and acid solution B is 20% acid.
How much of each solution should be used?
3.3 Graphing Inequalities

Graphing systems of inequalities using union and intersection,  and 
19) Alex earns $4.75 per hour plus 1% commission on his total sales.
a) Write an equation that describes Alex’s wages as a function of number of hours worked h and
total sales s.
b) If Alex works eight hours a day, how much merchandise must he sell to earn at least $60 a
day?
20) Let A = {2, 4, 6, 8, 13, 14, 15}, B = {2, 6, 7, 9, 12, 14, 15, 17}, and C = {4, 7, 8, 9, 12, 13, 17}
a) Find
A B
c) Find A  ( B  C )
21) Graph
b) Find
A B
d) Find ( A  B )  ( A  C )
x y
 1
4 5
22) Graph the solution set. {( x , y ) : y  x  3 and 0  x  4}  {( x , y ) : y   x  7 and 2  x  6}
23) Graph the solution set. { ( x , y ) : y  x 2 }
24) If (2, -6) and (-4, -12) are points on the graph of y = ax2 + b, what are the values of a and b?