Year 8AC9M8A02

Drawing a Line — Dual Intercept Method

Graph linear relations on the Cartesian plane; solve linear equations and one-variable inequalities using graphical and algebraic techniques; verify solutions by substitution.

Find where the line crosses each axis, then join them. Two points is all you need.

Worked example

e.g.

2y = 6x + 4

Write the equation in the form $y = mx + c$ $y = 3x + 2$
Calculate the $y$ intercept by substituting $x = 0$ $y = 3(0) + 2 \ \therefore \ y = 2$
Calculate the $x$ intercept by substituting $y = 0$ $0 = 3x + 2 \ \therefore \ x = -\tfrac{2}{3}$
Plot both intercepts and rule the line through them $(0; 2) \text{ and } (-\tfrac{2}{3}; 0)$

Practice

Find the $x$ intercept and the $y$ intercept:

y = 2x + 6

Answer

x \text{ int } (-3;0),\ y \text{ int } (0;6)

y = -x + 4

Answer

x \text{ int } (4;0),\ y \text{ int } (0;4)

y = 3x - 9

Answer

x \text{ int } (3;0),\ y \text{ int } (0;-9)

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

Answer

x \text{ int } (-4;0),\ y \text{ int } (0;2)

2y = 8x - 8

Answer

x \text{ int } (1;0),\ y \text{ int } (0;-4)

y = 10 - 5x

Answer

x \text{ int } (2;0),\ y \text{ int } (0;10)