Solution assignment 06 Linear functions and graphs

The line $l$ through the point $A(2,1)$ with slope $-2$ intersects the line:

$m: y=x+3$

in point $S$ .
Calculate the coordinates of $S$ .

First we determine the line $l$ . We use the formula:

$y-y_A=r(x-x_A)$

in which

$(x_A,y_A)=(2,1)$

are the coordinates of the point $A$ and $r$ is the slope of $l$ , so $-2$ . We find for $l$ :

$y-1=-2(x-2)$
$y=-2x+5$

In order to calculate the coordinates of $S$ , we solve ( $y$ -values of the intersection point $S$ are equal):

$-2x+5=x+3$
$3x=2$
$x=\displaystyle\frac{2}{3}$

and find the corresponding $y$ -coordinate:

$y=\displaystyle\frac{2}{3}+3=3\displaystyle\frac{2}{3}$

The result can seen in the figure.

Identify which line is which.