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MSA QUIZ TICKET for INV 1-3
So far we have studied lots of examples of linear equations. Some examples are:
y=x
y = 2x
y = 5 - 0.5x
y = 45
y = -3x - 6
Remember...... how can tell a relationship is linear from the equation, the table, the
graph? Can you give an example of a non-linear relationship?
X has an exponent other than 1, like x2
If you notice, all of the equations given in the examples are in the form y = mx + b.
For each equation, find the value of m and b:
y=x
y = 2x
y = 5 - 0.5x
y = 45
y = -3x - 6
m=1
m=2
m = -0.5
m=0
m = -3
b=0
b=0
b=5
b = 45
b = -6
Y-intercept
If you substitute 0 in for x in all of the equations, you will notice that y = b. This means
that the point (0, b) lies on the graph of that equation. The point (0, b) is called the yintercept.
Find the y-intercept for all of the examples:
y=x
y = 2x
y = 5 - 0.5x
y = 45
y = -3x - 6
0, 0
0, 0
0, 5
0, 45
0, -6
Coefficient of x
The m in y = mx + b is called the coefficient of x. The coefficient tells you how steep the
line will be and what direction the line will slant.
Order the equations from steepest to flattest:
y = 2x
y=x
y = 45
y = 5 - 0.5x
y = -3x - 6
Which equations which slant upward (bottom left to upper right)?
y = 2x
y=x
Which equations which slant downward (bottom right to upper left)?
y = 5 - 0.5x
y = -3x - 6
Which equations will be flat?
y = 45
ARE you ready for the test ??? Try these.
Solve each equation to find the value of x. SHOW ALL STEPS!!! (2 points each)
a. 6x + 5 = 47
b. 2x + 12 = 5x
Does it
work?
c.
Does it
work?
-5 -5
6x =42
÷6
÷6
x= 7
-2x
Does it
work?
3(x + 3) = 24
-2x
12 = 3x
÷3 ÷3
4=x
d. 3x + 17 = 25 – 6x
3x+9 =24 distribute
-9 -9
3x =15
÷3
÷3
x= 5
Does it
work?
+6x
+6x
9x + 17 = 25
-17 -17
9x = 8
÷9
÷9
x = 8/9 or .888
e. 3.5 = 2x – 2.5
f. -4(2x – 11) = 3x
+2.5 +2.5
Does it
work?
6 =2x
÷2
÷2
3= x
Does it
work?
-8x + 44 =3x distribute
+8x
+8x
44 = 11x
÷11 ÷11
4=x
Phoebe is selling lemonade for 3 dollars a glass. THIS IS HER REVENUE
She borrowed $21 for a stand and it costs her $1.50 per glass in materials. THIS IS HER COSTS.
When will Phoebe’s revenues be equal to her costs? Show Algebraic solution.
1) Write the two equations
Income:
Expenses:
2) Set the expressions equal to each other
3) Solve the new equation
3x = 21 + 1.5x
-1.5x -1.5x
1.5x = 21
÷1.5 ÷1.5
x=14
4) Find the coordinate point
Since x=14
y= 3(14)=42
Check
21 + 1.5(14) =42
Y= 42 so (14,42)
5) Interpret the meaning
Y= 3x
Y= 21 + 1.5x
That means Phoebe will have to sell 14
cups of lemonade to make $42. At that point
she would have also spent $42 in supplies so
she would break even.
Revenue – costs = profit
3x – (21+ 1.5x) = 0
3(14) – (21+ 1.5(14)) = 0
REVIEW: Slope(m, rate), y-intercept(0,b), linear form y=mx+b