Perpendicular linear graphs

Maths

The work on gradient in this unit is expanded further in the future unit by considering gradient as the rate of change and interpreting this in context. The gradient of the tangent is introduced as a way of estimating the gradient of a curve.

In the prior unit, pupils drew a linear graph from its equation and related the features of the graph to its equation. In this unit, pupils consider equations that produce parallel or perpendicular graphs and how their equations relate to each other.

Linear graphs

Two lines which are always the same distance apart.

Two lines which are reflections of each other in the $$y$$-axis.

Two lines which intersect at right-angles.

Which of these statements best describes perpendicular lines?

Their gradients are reciprocals of each other. 

Which of these statements is true for perpendicular lines?

Which of these diagrams show two lines which are perpendicular? 

A shape is a rectangle iff it is a square.

A triangle has a right-angle iff Pythagoras' theorem holds. 

A number is an integer iff it is positive.

Two lines are perpendicular iff their gradients have a product of -1.

Which of these statements is a correct use of the phrase 'if and only if' (iff)?

Which of these is an expression for the length of the line AB?

$$2(m_1 )^2 + 2(m_2 )^2   = 2− 2m_1m_2$$

$$(m_1 ) + (m_2 )  + 1 = (m_1 ) + (m_2)− m_1m_2$$

Which of these is equivalent to the equation $$(m_1 )^2 + (m_2 )^2  + 2 = (m_1 )^2 + (m_2)^2− 2m_1m_2$$?

If the gradients of two lines are a zero pair, the lines are parallel.

Parallel lines have the same $$y$$-intercept. 

Parallel lines intersect at right angles. 

Which of these statements is true for parallel lines?

The equation of the line drawn below is $$y =$$ {{}}$$x -1$$.

The equation of the line drawn below is $$y = -{4\over 5}x +$${{}}.

Using Pythagoras' theorem, the length of this line segment is {{ }} units.

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