Exercises: Linear functions, zeros, axis intercepts

$y = 3 x - 2$

Set $y = 0$ to determine the zero point. This is the point where the line intersects the $x$ -axis.

Proceed in the same way for the second line.

$y$	$=$	$- \frac{3}{4} x + 1$
	↓	Set y=0 to determine the zero.
$- \frac{3}{4} x + 1$	$=$	$0$	$- 1$
$- \frac{3}{4} x$	$=$	$- 1$	$: (- \frac{3}{4})$
$x$	$=$	$\frac{1}{\frac{3}{4}}$
	↓	You divide by a fraction -> multiply by the reciprocal value
$x_{N2}$	$=$	$\frac{4}{3}$

Set the two function equations equal. The straight lines intersect where both have the same $y$ -value at the same $x$ -position.

$3 x - 2$	$=$	$- \frac{3}{4} x + 1$	$+ \frac{3}{4} x + 2$
$3 x + \frac{3}{4} x$	$=$	$1 + 2$
$3.75 x$	$=$	$3$	$: 3.75$
$x$	$=$	$\frac{3}{3.75}$
$x_{S}$	$=$	$0.8$
	↓	Plug $x_{S}$ into one of the two functions.
$y$	$=$	$3 \cdot 0.8 - 2$
$y$	$=$	$2.4 - 2$
$y_{S}$	$=$	$0.4$

$\Rightarrow S (0,8 | 0,4)$

The intersection point is at $S (0.8 | 0.4)$ .