Solution assignment 07 Linear functions and graphs

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Assignment 7

The line l goes through the points A(2,1) and B(0,3) and intersects the line:

m: y=2x

in point S.
Calculate the coordinates of S.

Solution

The equation of the line l is not yet known and has to be determined. We can calculate the slope r of l with:

r=\displaystyle\frac{y_B-y_A}{x_B-x_A}=\displaystyle\frac{3-1}{0-2}=-1

Now we have the slope of l we can calculate the equation and therefore we have to choose one of the points A and B. We choose the point B, so:

y-y_B=r(x-x_B)
y-3=-1(x-0)
y=-x+3

We find the x-coordinate of the intersection point S by solving:

2x=-x+3
x=1

and thus we have:

y=2

The intersection point S has the coordinates (1,2).
Check this in the figure.

2x en -x+3

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