 # Math - Gradient and Intercept

In this lecture, we learnt about Cartesian coordinates and used points on our line to work out the gradient of our lines.

We also looked at the intercept points, where our line crosses the x- and y- axes.

For your challenge, you need to;

• Draw the line for currentFuel/time, where the maxFuel = 150 and burnRate = 2
• Find the the x- and y- intercept points
• label 4 co-ordinates on your graph
• work out the gradient of the line

How did you get on?

Every second the rocket looses -2, for a max of 75 seconds.

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So I found that for maxFuel = 150 and burnRate = 2, the tank lasts 75 seconds.
The slope is of -2.
And I have this coordinates: (5,140). (25,100). (50,50). (60,30).

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Points = (0,150) (30, 90) (45, 60) (75, 0)
x intercept = 75
y intercept = 150
slope = -2

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Here is my respond:

you mention during the course to draw these by hand. I have TI-Nspire calculator on my computer so is it fine if I use it for this?

Great work @Mikapo.

There are no requirement for you to draw your graphs by hand if you don’t want to.

I mainly encourage it at this stage because it can be very easy to rely on technology to do all the work for us and that may not always be an available option when we need it.

However, if you’re already comfortable with reading and drawing graphs then feel free to use a graphing calculator or other digital tools. If you feel like you could use the practice of doing things the old fashioned way then definitely push yourself to give it a go.

It’s really up to you with how you approach your learning, so use whichever workflow you find the most useful.

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At 75 seconds, the fuel tank reaches 0.

x intercept: (75,0)
y intercept: (0,150)
Some labeled coordinates: (200,110) (30,90) (40,70) (50,50)
Slope = -2, which makes sense because it is the same as the burn rate.

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Labeled points:
(0,150)
(25,100)
(65,20)
(75,0)

X-intercept: (75,0)
Y-intercept: (0,150)

slope: -2

m = 150, b = 2, t = 75, c = 0.
My 4 Coordinates are (15, 120), (30, 90), (50, 50), (65, 20).
And the Gradient of the Slop is -2.

Good morning!

Challenge Time:

• Finding (t) for c = 0
t = ( c - m ) / - b
= ( 0 - 150 ) / -2
= - 150 / -2
[ t = 75 ]

final intercept = ( 75, 0 )

• Finding (c) = m - ( b * t )
for t = 50
c = 150 - ( 2 * 50)
c = 150 - 100
[ c = 50 ]
intercept = ( 50, 50)

• Gradient ( y2 - y1) / ( x2- x1 )
( 0 - 50) / ( 75 - 50)
-50 / 25

Here are my results:

X- intercept: 150
Y- intercept: 75
4 co-ordinates: (10,130)(35,80)(37.5,75)(50,50)

Here’s my attempt at the Gradient and Intercept challenge:

For the slope, I just took two of my points (P1 and P2) and used the formula to find it:
A1a. (100 - 70) / (25 - 40)
A1b. 30 / -15
A1c. -2

Therefore, our graph has a slope of -2.

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x intercept is 75 and y intercept is maxFuel (150)
I picked 4 time values for calculating the c and thus the coordinates:
(20,110)
(25,100)
(40,70)
(60,30)
the slope result was -2 or a decay of 2

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Points = (0,150) (30, 90) (45, 60) (75, 0)
x intercept = 75
y intercept = 150
slope is of -2