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Year 8AC9M8A02

Drawing a Line — Gradient 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.

Worked example

e.g. 2y=−4x+42y = -4x + 4
  1. Write the equation in the form y=mx+cy = mx + cy=−2x+2y = -2x + 2
  2. Write the gradient in fraction formy=−21x+2y = -\tfrac{2}{1}x + 2
  3. Start at cc on the yy axis. That is your first point(0;2)(0; 2)
  4. Numerator is units up or down. Denominator is units right. Here: 2 down, 1 rightdown 2, right 1\text{down } 2, \text{ right } 1
  5. Mark the second point and rule the line(1;0)(1; 0)
    Starting at the y intercept and stepping down two and right onexyy = -2x + 2startdown 2, right 1

Practice

Give the yy intercept and the step (up or down, then right):

1
y=3x+1y = 3x + 1
Answerstart (0;1), up 3 right 1\text{start } (0;1),\ \text{up } 3 \text{ right } 1
2
y=−x+5y = -x + 5
Answerstart (0;5), down 1 right 1\text{start } (0;5),\ \text{down } 1 \text{ right } 1
3
y=23x−2y = \tfrac{2}{3}x - 2
Answerstart (0;−2), up 2 right 3\text{start } (0;-2),\ \text{up } 2 \text{ right } 3
4
y=−34xy = -\tfrac{3}{4}x
Answerstart (0;0), down 3 right 4\text{start } (0;0),\ \text{down } 3 \text{ right } 4
5
2y=6x−82y = 6x - 8
Answery=3x−4: start (0;−4), up 3 right 1y = 3x - 4: \ \text{start } (0;-4),\ \text{up } 3 \text{ right } 1
6
y=4−2xy = 4 - 2x
Answerstart (0;4), down 2 right 1\text{start } (0;4),\ \text{down } 2 \text{ right } 1
Next step
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