The graph of the line passes through the points (0,6) and (3,0). What is the equation of this line?

The graph of the line passes through the points (0,6) and (3,0)

(a) The equation of the line AB:

The slope of the line is;

Slope = change in y ÷ change in x = = -2

Picking another point (x,y) on the line;

Slope = = -2

Cross-multiplying gives;

y = -2x + 6 (which is the equation of line AB)

(b) The gradient of the line perpendicular to AB:

The products of slopes of two perpendicular lines = -1

Since the slope of our line = -2,

We assume the perpendicular line has a slope of a,

So a × -2 = -1

a =

So the slope (gradient) of the perpendicular line =

(c) The equation of the line passing through point A and perpendicular to AB:

Point A is the point (0,6) on the graph.

A line that passes through this point and is perpendicular to AB must have a gradient (or slope) of

Taking another point (x,y) on the perpendicular line;

Slope = change in y ÷ change in x

=

Cross-multiplying gives;

2y - 12 = x

2y = x + 12

y = + 6 (the equation of the perpendicular line via A)

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