Session 1 Check Your Understanding Linear Equations

Published

September 8, 2026

Check your understanding of Linear Equations

Try these questions to see whether you have understood the main ideas of this session.

Short-answer questions

  1. For each equation, state the gradient and the y-intercept:

    • y=3x-4
    • y=-\frac{1}{2}x+5
    • 2x+5y-10=0

  2. Explain what the gradient tells you about a straight line. In your answer, mention both the sign and the size of the gradient.

  3. A line has equation y=mx+3. What is the effect of changing m while keeping the y-intercept fixed? Describe the graph in words.

  4. The equation y=2x-5 is given. Find:

    • the y-intercept,
    • the x-intercept,
    • another point on the line.

  5. Solve the equation 3x+2y=12 for y. Then identify the gradient and y-intercept of the line.

  6. For each pair of equations, decide whether the lines are parallel, coincident, or intersecting:

    • y=2x+1 and y=2x-3
    • y=3x+2 and 2y=6x+4
    • y=x+2 and y=-x+2

  7. A line passes through the points (1,4) and (3,10). Find:

    • the gradient,
    • the equation of the line,
    • whether it passes through (5,16).

  8. Solve the simultaneous equations using substitution: y=2x+1, \qquad 3x+y=11.

  9. Solve the simultaneous equations using elimination: 2x+3y=13, \qquad 4x+3y=17.

  10. Explain the difference between the algebraic and geometric interpretation of a solution to a single linear equation.

  11. Two lines have equations 2x+y=5 and x-y=1. Find the point where they intersect and explain why this point is a solution to both equations.

  12. A student says: “If two linear equations have the same gradient, then they must have infinitely many solutions.” Is this statement true or false? Explain your answer.

Challenge questions

  1. The line through (2,5) and (6,13) is written in the form y=mx+c. Find m and c.

  2. A line has equation 3x-2y+12=0. Find the x-intercept and y-intercept, and describe the line in words.

  3. The equations of two lines are y=4x-7 \quad \text{and} \quad 4x-y+3=0. Determine whether the lines are parallel, coincident, or intersecting, and justify your answer.

  4. Explain why the complete set of solutions to a single linear equation is represented by a straight line on a graph.

Quick reflection

  • I can identify the gradient and y-intercept from an equation.
  • I can describe the meaning of a linear equation algebraically and geometrically.
  • I can solve simultaneous equations and explain what the solution means graphically.
  • I can decide whether two linear equations have one solution, no solution, or infinitely many solutions.