Line Slope Finder

Lessons

These lessons cover everything you need to find the slope of a line and write its equation. Each one has worked examples, and most link to the Slope Finder so you can see the example on a graph and move the points yourself.

Start here

  1. What is slope? What slope measures, and positive, negative, zero and undefined slopes.
  2. The slope formula: m = (y₂ − y₁) / (x₂ − x₁), and how to avoid sign mistakes.
  3. Zero and undefined slope: horizontal and vertical lines.

Equations of a line

  1. Slope-intercept form: y = mx + b, the most common form.
  2. Point-slope form: y − y₁ = m(x − x₁), for when you know one point and the slope.
  3. Standard form: Ax + By = C, and converting between forms.

Using slope

  1. Finding the equation of a line from a graph
  2. Finding slope from a table of values
  3. Parallel and perpendicular lines
  4. Practice problems with answers

Two lines at once: systems of equations

  1. Solving systems of equations by graphing: the solution is where the lines cross.
  2. The substitution method: make one variable the subject and substitute it.
  3. The elimination method: add or subtract the equations to remove a variable.
  4. No solution or infinitely many solutions: parallel lines and identical lines.
  5. Systems of equations word problems: tickets, phone plans and more.

To check any system, use the Intersection Finder.

Quadratic equations

  1. Solving quadratic equations by factorising: from (x + 2)(x − 3) = 0 to splitting the middle term.
  2. The quadratic formula: x = (−b ± √(b² − 4ac)) ÷ 2a, the discriminant, and which method to choose.
  3. Solving quadratic equations by intersecting lines: rearrange to x² = mx + k and find where the line meets y = x².

Check any quadratic with the Quadratic Solver, which shows all three methods.

Data and lines of best fit

  1. Scatter graphs and correlation: positive, negative and no correlation, and the correlation coefficient r.
  2. Drawing and using a line of best fit: by eye, its equation, and predictions.
  3. The least squares regression line: the exact line of best fit, worked by hand.

Try it with your own data in the Line of Best Fit calculator.