Year 9AC9M9A03

Determine a Straight Line Equation

Find the gradient of a line segment, the midpoint of the line interval and the distance between 2 distinct points on the Cartesian plane.

Worked example

e.g.

\text{determine the equation of the line passing through } A(2;3) \text{ and } B(3;9)

Calculate the gradient of the line $m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ $m = \tfrac{9-3}{3-2} = \tfrac{6}{1} = 6$
Substitute into $y = mx + c$ $y = 6x + c$
Find a coordinate set on the line and substitute to calculate $c$ $3 = 6(2) + c \ \therefore \ c = -9$
Write the equation $y = 6x - 9$

Calculate the equation of the line passing through the following points:

(1;3) \text{ and } (6;9)

Answer

y = \tfrac{6}{5}x + \tfrac{9}{5}

(1;3) \text{ and } (9;6)

Answer

y = \tfrac{3}{8}x + \tfrac{21}{8}

(1;3) \text{ and } (4;0)

Answer

y = -x + 4

(6;9) \text{ and } (4;0)

Answer

y = \tfrac{9}{2}x - 18

\text{parallel to } 2y = 3 + x \text{ through } (2;3)

Answer

y = \tfrac{1}{2}x + 2

\text{perpendicular to } y = 2x \text{ through } (1;0)

Answer

y = -\tfrac{1}{2}x + \tfrac{1}{2}

\text{perpendicular to } x = y + 3 \text{ through } (0;0)

Answer

y = -x

\text{parallel to } y - 6 = x - 3 \text{ through } (1;1)

Answer

y = x

\text{parallel to } y = 3 + 2x \text{ through } (2;1)

Answer

y = 2x - 3

\text{perpendicular to } x + 2y = 5 \text{ through } (4;1)

Answer

y = 2x - 7