Question

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

Answer 1

Answers plus Step-by-step explanations:

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 = $\frac{0 - 6}{3 - 0}$ = -2

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

Slope = $\frac{y - 0}{x - 3}$ = -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 = $\frac{1}{2}$

So the slope (gradient) of the perpendicular line = $\frac{1}{2}$

(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 $\frac{1}{2}$

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

Slope = change in y ÷ change in x

$\frac{1}{2}$ = $\frac{y - 6}{x - 0}$

Cross-multiplying gives;

2y - 12 = x

2y = x + 12

y = $\frac{x}{2}$ + 6 (the equation of the perpendicular line via A)