Sec 1 graphs: coordinates and straight lines

Coordinates tell you where a point is. For a straight line, the gradient tells you how y changes when x increases by one unit.

What this guide covers

Selected Sec 1 N6 skills: ordered pairs, straight-line equations, y-intercepts and gradient. Quadratic curves and tangent gradients are later work.

Keep the axes and order visible

A point is written (x,y). On y=mx+c, c is the value of y when x=0; m is the rise divided by the corresponding run. Subtract coordinates in the same order.

Read a line from its equation

For y=2x−3, find y when x=−1 and x=2. State its y-intercept and gradient.

  1. At x=−1, y=2(−1)−3=−5; at x=2, y=4−3=1.
  2. When x=0, y=−3, so the y-intercept is (0,−3).
  3. The coefficient of x is 2: y rises by 2 for each increase of 1 in x.

Check: From (−1,−5) to (2,1), rise/run =63=2.

Try it yourself

Work on paper, then compare the steps. These checks do not establish mastery.

A line passes through (0,4) and (3,10). Find its gradient and equation.

Gradient =(10−4)(3−0)=2. At x=0, y=4, so the equation is y=2x+4. Check: at x=3 it gives 10.

For y=−x+5, is (2,3) on the line? State the gradient and y-intercept.

At x=2, y=−2+5=3, so (2,3) is on it. Gradient is −1 and y-intercept is (0,5).

Where this connects

Sources and scope

Original Mentora examples and checks aligned to Sec 1 N6 in the MOE G2/G3 Mathematics syllabus. The equations and coordinates were authored for this guide.

MOE G2 and G3 Mathematics syllabuses ↗