Gradients & the Equation of a Line

A personalised practice quiz has also been sent to Alex.

Lesson Summary

Alex had a great session today working through gradient calculations and the equation of a line. He demonstrated strong conceptual understanding of rise over run and built real confidence solving problems step by step, finishing the lesson by finding the full equation of a line from two points on his own.

What Alex did well

• Calculating the gradient from two coordinate points using m = rise/run.

• Explaining why a steeper line has a larger gradient.

What needs improving

• Substituting a known point into y = mx + b to find the y-intercept.

• Keeping track of negative signs when the line slopes downwards.

What's Next?

Next lesson we'll practise finding y-intercepts with negative gradients, then move on to parallel and perpendicular lines. A few minutes on this week's quiz will help lock in today's progress.

Finding Gradients

Alex used m = rise/run to calculate gradients from coordinate pairs, correctly solving m = 6/3 = 2 with the triangle diagram.

Equation of a Line

Alex substituted the gradient into y = mx + b and found the y-intercept from a known point, arriving at y = 2x.