Exercises: Intersection of two lines

Determination of intersection points

Consider the following two lines $g$ and $h$ .

Determine the line equations of $g$ and $h$ .

For this task you need the following basic knowledge: Line equation
$y = m x + t$
The parameter $m$ is the slope of the line. The parameter $t$ is the $y$ -axis intercept.
Line $g$ :
$y = m_{g} x + t_{g}$
The line $g$ has slope $- \frac{3}{2}$ , so $m_{g} = - \frac{3}{2}$ .
$y = - \frac{3}{2} x + t_{g}$
It intersects the $y$ -axis at $\frac{9}{2}$ , so $t_{g} = \frac{9}{2}$ .
$y = - \frac{3}{2} x + \frac{9}{2}$
Line $h$ :
$y = m_{h} x + t_{h}$
The line $h$ has slope $2$ , so $m_{g} = - \frac{3}{2}$ $m_{h} = 2$
$y = 2 x + t_{h}$
It intersects the $y$ -axis at $1$ , so $t_{h} = 1$ .
$y = 2 x + 1$
Read off the intersection point.

For this task you need the following basic knowledge: Lines in coordinate systems
Reading off the intersection point
From the plot, we may read off the intersection point $SP (1 | 3)$ .

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