- 1. What Is Gradient? Steepness and Direction
Describe what gradient (m) measures, calculate it from a grid using rise ÷ run, classify a gradient as positive, negative, or zero from a line's direction, and compare steepness using the size of the gradient.
- 2. Reading the Equation: Gradient and y-Intercept
Read the gradient m and the y-intercept c directly from a linear equation in the form y = mx + c, spot hidden values such as the gradient of y = x, and rearrange any linear equation into y = mx + c before reading off m and c.
- 3. Drawing Straight-Line Graphs
Build a table of values from a linear equation, plot the points and draw an accurate straight line, rearranging the equation into y = mx + c first when necessary, and verify the finished graph using its gradient and y-intercept.
- 4. Writing the Equation from a Graph
Write the equation of a straight line from its gradient and y-intercept, and read m and c from a drawn graph — choosing reliable lattice points — to assemble its equation in the form y = mx + c.
- 5. Equation of a Line Given Gradient and One Point
Find the y-intercept c by substituting a known point into y = mx + c, write the full equation of a line from its gradient and any point, use the point-gradient formula y − y1 = m(x − x1), and extract a gradient hidden inside another equation.
- 6. Equation of a Line Given Two Points
Find the equation of a straight line through two given points by chaining the two-point gradient formula with point substitution to find c, recognising the shortcut when a point lies on the y-axis, and verifying against both points.
- 7. Where Lines Meet the Axes — x-Intercept and y-Intercept
Find where a line crosses the y-axis by setting x = 0 and where it crosses the x-axis by setting y = 0, state both intercepts as coordinate points, and use the two intercepts to sketch a line quickly.
- 8. Point of Intersection of Two Lines
Find where two lines cross by recognising that the intersection satisfies both equations at once, using the substitution method and the elimination method, and verifying the point in both original equations.
- 9. Gradient of a Curve — Drawing and Reading Tangents
Explain why the gradient of a curve changes from point to point, draw a tangent to a curve at a given point, calculate the curve's gradient from the tangent's rise over run, and recognise that the gradient at a turning point is zero.
