Exercises: Finding line equations

The general line equation is:

$y = m \cdot x + t$

Read the y-intercept $t$ , i.e. the point at which the straight line intersects the y-axis, from the drawing.

$t = - 1$

Find two points with (at best) integer coordinates.

$P (2 | 2)$ and $Q (4 | 5)$ are on the line

There are two ways to determine the gradient $m$ :

1. $m = \frac{y_{Q} - y_{P}}{x_{Q} - x_{P}}$

Plug in the coordinates of $P$ and $Q$ .

$m = \frac{5 - 2}{4 - 2} = \frac{3}{2} = 1.5$

2.

Zeichnung des Steigungsdreiecks zwischen Punkten P und Q

Draw a slope triangle between the points. The vertical distance is the numerator, the horizontal distance is the denominator of the fraction that describes the gradient.

$m = \frac{senkrecht}{waagerecht} = \frac{3}{2} = 1.5$

The line equation is therefore given by :

$g (x) = \frac{3}{2} \cdot x - 1 = 1.5 x - 1$