Using dynamic software to explore linear relationships | Maths

Starter quiz

Relationships in the form of $y=mx+c$ will give us a ______.

curve when graphed

straight line graph ✓

increasing sequence

increasing graph
What is the gradient of this line?

$-2$

$-1$

$1$

$2$

$3$ ✓
Which of these coordinates is $(0,3)$ ?

A

B ✓

C

D
Which of these coordinates sits on the $y$ -axis?

$(-4,2)$

$(-3,0)$

$(-2,-2)$

$(-1,-4)$

$(0,-6)$ ✓
This table of values will plot a linear relationship with what gradient?

'+4' ✓
This table of values will plot a linear relationship with what gradient?

'+2' ✓

For relationships in the form $y=mx+c$ the value of $m$ determines the ______.

coordinates

$y$ -intercept

$x$ -intercept

scale of the axes

gradient ✓
What of these statements will be true about the lines $y=3x$ , $y=7x$ , and $y=-2x$ ?

They will all have a different gradient. ✓

They will be parallel lines.

One and only one of the lines will have a negative gradient. ✓

They will all have a different $y$ -intercept.
What is the equation of this line?

$y=2x$

$y={1\over2}x$ ✓

$y=x+2$

$y=x+{1\over2}$
Which statements are true about the lines $y=x+5$ , $y=x+9$ , and $y=x+0.5$ ?

They have the same gradient. ✓

They are parallel lines. ✓

The have the same $y$ -intercept.

They have common coordinates.
The lines $y=4-7x$ and $y=-0.1-7x$ have the same ______.

'gradient' ✓
Calculate the equation of the line.

$y=0.45-0.3x$ ✓

$y=0.45-1.5x$

$y=0.5-0.3x$

$y=0.3-0.45x$

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Dynamic software can be used to investigate how the gradients affects the line.
Dynamic software can be used to investigate how the intercept affects the line.
Dynamic software can be used to investigate connections between lines, coordinates, tables and algebraic representations

From the line $y=x$ to $y=x+1$ to $y=x-1$ the lines are moving left/right rather than up/down.

It can be shown by using a $(x,c)$ coordinate in desmos. That coordinate moves up and down with the change in ' $c$ '.

Gradient - The gradient is a measure of how steep a line is.
Intercept - An intercept is the coordinate where a line or curve meets a given axis.