Solution assignment 06 Linear functions and graphs

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Assignment 6

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.

Solution

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.

x+3=-2x+5

Identify which line is which.

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