FINDING GRAPH NAMES WHEN

GIVEN CO-ORDINATESSLIDESHOW 30, MATHEMATICS

MR RICHARD SASAKI, ROOM 307

OBJECTIVES

• Understand how to find the name of a graph when given its gradient and a pair of co-ordinates• Understand how to find the name of a graph

when given two pairs of co-ordinates

THE GRADIENT

We know that the gradient (the line’s steepness) is always identical to the -coefficient in the graph’s name. We can see that the line

goes through (-1, -1) and (0, 2) clearly so we can make a gradient triangle.

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This implies that and we get from the y-intercept.

A PAIR OF CO-ORDINATESWhat if instead of having the y-intercept, we have a pair of co-ordinates?

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If we know the gradient is 3 and the line passes through (-1, -1), how do we find the graph name with just this?

We simply put the co-ordinate values () into the equation.

A PAIR OF CO-ORDINATESWe know that the gradient is 3, so we get and we have (-1, -1), so and .

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Let’s substitute and into .

We get so .Therefore, .

EXAMPLELet’s try another example, this time with no graph.

On a graph, a line has a gradient of 2 and passes through co-ordinates (-5, 3). Calculate the name of this line in the form .

All we have to do is substitute and into the equation to find .

We get .

ANSWERS

𝑦=2 𝑥+1𝑦=3 𝑥−10𝑥

𝑦12

(0 ,1)𝑦=2 𝑥+1

1

(0 ,0)

𝑦=𝑥−1𝑦=19𝑥=

133

1 , 𝑦=𝑥+1

𝑦=5 𝑥+11𝑦=−3𝑥+30𝑦=4 𝑥

TWO PAIRS OF CO-ORDINATES

Hopefully, you saw (as in Question 7), you can calculate the name of a line with two pairs of co-ordinates and no gradient.Here we have 4 numbers, but what do we do with them?𝐺𝑟𝑎𝑑𝑖𝑒𝑛𝑡 (𝑎 )=¿𝑦2−𝑦 1𝑥2−𝑥1

It doesn’t matter which way around things are. We could calculate if we wanted too but we can’t mix them up.

EXAMPLE

A straight line goes through two points, (5, 2) and (7, 8). Calculate the name of the line in the form .

First, let’s find the gradient, .𝐺𝑟𝑎𝑑𝑖𝑒𝑛𝑡 (𝑎 )=¿𝑦2−𝑦 1𝑥2−𝑥1¿8−27−5¿3Great! There’s done, but how do we find ?

Same as before! Let’s substitute!

Let’s consider and .

We get .

𝑦=5 𝑥−14 𝑦=−3𝑥+4𝑦=4𝑦=−

12𝑥+2 𝑦=−2𝑥−1𝑦=−

12𝑥+4

𝑦=−2𝑥+16 𝑦=−2𝑥+4 𝑦=−𝑥−9