IB Maths AI 2.1 Notes

Lines & gradients

In this topic, you study different forms of the equation of a straight line, gradients, intercepts, and the conditions for parallel and perpendicular lines.

The main forms required are gradient-intercept form, general form and point-gradient form.

The gradient describes the steepness of a line. It tells us how much the $y$-value changes for each unit increase in $x$.

$m=\frac{(y_2-y_1)}{(x_2-x_1)}=\frac{\Delta x}{\Delta y}$

The value of the gradient is indicative of the form of the line:

• If $m\gt 0$, the line rises from left to right.
• If $m\lt 0$, the line falls from left to right.
• If $m=0$, the line is horizontal.
• A vertical line has equation $x=a$ and has undefined gradient because the denominator in the gradient formula would be $0$.