2TH/vwo lesson 3 - Equations/Graphs

• Middelbare school
• vwo
• Leerjaar 1

First let's look at the steps we need to plot a linear graph

Formula

Table

Graph

Sometimes we only have a graph and not the formula.

What do we do then?

Graph

Table 

Formula

Steps

1. Find some values on the graph that can be read off easily
2. Make a table
3. Find gradient and y-intercept
4. Make a linear formula

Remember this?

• Make a table with values of t on the top row and corresponding values of N on the bottom row

                   t    0    1      2    3    4

                   N  2   2.5   3  3.5  4

• Use the table to find the y-intercept (value of N when t=0)  so here y-intercept = 2
• Use the table to calculate the gradient           increase in N /increase in t = 1/2 or 0.5
• Fill these values into the standard formula y=ax + b where a is the gradient and b is the y-intercept
• y = 0.5x + 2

What is the difference between a formula and an equation?

Formula - is a rule about how you calculate for all values

Equation - When a formula has a specific answer.

You can solve the equation to find which value of the variable gives the correct answer.

How do you find a value that is not easy to read off a graph?

Use the steps above to find the linear formula

Write down the corresponding equation

Solve the equation

The graph corresponds to the growth of a seedling. After how many days is the seedling 50cm high?

Graph

Table

time in days (t)       0      2     4     6  

height in cm  (H)    5    10    15   20

y-intercept = 5

gradient = 5/2 =2.5

formula: H = 5 + 2.5t

but H=50

so equation 50 = 5 + 2.5t

Solving

45 = 2.5t

45/2.5 = 18 = t 

so after 18 days the seedling is 50cm high

What is a formula?

What is an Equation?

How many coins weigh 875 grams?

1. 75
2. 7.5
3. 100
4. 65

Here is the graph for the formula
b = 10 + 5t

Solving the equation
21.50 = 10 + 5t
gives
t=?

1. 3.2
2. 2.3
3. 11.5
4. 5

L= 3m +12
L = 4m + 12
L = 1/3m + 12
What are the values of m when L=48?

1. m=3, m=4, m=1/3
2. m=16, m=12, m= 144
3. m=1/3, m=4, m=3
4. m=12, m=9, m=108

More than 1 mistake

ex 15,17,18

ex 38,40, T3

ex B4,B5

Only 1 mistake

Ex 38,40, T3

ex B4,B5

All correct

ex T3,B4,B5

What do you remember from today's lesson?

Graphs