# 1819 G2X §9.3

Which exercises should we discuss on the board?
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Slide 1: Mind map
WiskundeMiddelbare schoolhavo, vwoLeerjaar 2

This lesson contains 11 slides, with interactive quizzes and text slides.

Lesson duration is: 50 min

## Items in this lesson

Which exercises should we discuss on the board?

#### Slide 1 -Mind map

What are the coordinates of the point of intersection?

#### Slide 2 -Open question

Finding the point of intersection
We can easily read off the point of intersection for the
graphs on the right, because the point of intersection is
a grid point.

What if the point of intersection is not visible or
not a grid point?

#### Slide 3 -Slide

Finding the point of intersection
How can we find the point of intersection for
these graphs?

Remember that a point of intersection is
a point on both graphs that have the same
horizontal and the same vertical coordinate.

We can use an equation to find the horizontal
coordinate!

#### Slide 4 -Slide

Finding the point of intersection
First we need a formula for each line.
The green line:       y-intercept = 1
gradient = 1 ÷ 2 = 0.5
formula: y = 0.5x + 1

The blue line:         y-intercept = -4
gradient = 4 ÷ 5 = 0.8
formula: y = 0.8x - 4

#### Slide 5 -Slide

Finding the point of intersection
y = 0.5x + 1                     y = 0.8x - 4
As the graphs should both have the same y-value in the
point of intersection, we can make the equation:
0.5x + 1 = 0.8x - 4
Solve this:                                1 = 0.3x - 4
5 = 0.3x
x =

This means the horizontal coordinate of the
point of intersection is

1632
1632

#### Slide 6 -Slide

Finding the point of intersection
y = 0.5x + 1                     y = 0.8x - 4
The horizontal coordinate of the point of intersection is

To find the vertical coordinate we fill in x =
in each formula

So the coordinates of the point of intersection are
1632
1632
y=0.51632+1=931
y=0.816324=931
(1632,931)

#### Slide 7 -Slide

Finding the point of intersection
1) Make an equation by making both formulas equal to each other.
2) Calculate the horizontal coordinate by solving the equation.
3) Calculate the vertical coordinate  by filling in the horizontal coordinate in both formulas
4) Write down the point of intersection (.... , ....)

#### Slide 8 -Slide

Sketching graphs
If you want to plot a graph, you first make a table, then a coordinate system and your graph should be very precise.

If you sketch a graph, your graph does not have to be very precise. It should show where it intersects the vertical axis, and if the graph is rising or falling.

Sketches can be useful for getting an idea about where the point of intersection is and when solving inequalities (§9.5).

#### Slide 9 -Slide

Example
Sketch the graphs of the
formulas y = 2x + 5 and y = 3x - 1
in one coordinate system.

- both rising
(blue faster than green)
- y-intercepts 5 and -1

#### Slide 10 -Slide

HW Monday
Make and correct §9.3