Question

Use technology to obtain approximate solutions graphically. All solutions should be accurate to one decimal place. (Zoom in for improved accuracy.)

Find the intersection of the line through (0, 1) and (4.3, 2) and the line through (2.1, 3) and (5.4, 0).
(x, y) =

Answer 1

(x, y) ≈ (3.4, 1.8)

Explanation:

You want the point of intersection of the lines through (0, 1), (4.3, 2) and (2.1, 3), (5.4, 0).

Graph

The first attachment shows a graph of the lines and the coordinates of the point of intersection. The solution is ...

(x, y) ≈ (3.42, 1.8)

(x, y) = (3.4, 1.8) . . . . accurate to 1 decimal place

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Additional comment

For each pair of points, the equation of the line can be written as ...

(y2 -y1)(x -x1) -(x2 -x1)(y -y1) = 0

(2 -1)(x -0) -(4.3 -0)(y -1) = 0 ⇒ x -4.3y +4.3 = 0

and

(0 -3)(x -2.1) -(5.4 -2.1)(y -3) = 0 ⇒ -3x -3.3y +16.2 = 0

The calculator result in the second attachment shows the exact solution to be ...

(x, y) = (3 229/540, 1 43/54) ≈ (3.42407, 1.79630)