Sue is drawing two lines on a coordinate plane. She begins the first line at the origin and ends at (4,3). She begins the 2nd line at (0,4) and ends at (3,0). Where will these lines intersect?

If Sue draws these lines very carefully on a graph with appropriate grid spacing using a sharp pencil, she might be able to determine that the point of intersection is (1.92, 1.44).

Attached is the result of graphing these lines in a graphing tool that is capable of showing the coordinates of the point of intersection.

Analytic solution

Sue can probably recognize that the equations of the lines are ...

y = 3/4x . . . . . . . a proportional relation

and

x/3 +y/4 = 1 . . . . . the intercept form of the equation of a line

These can be written in general form as ...

3x -4y +0 = 0

4x +3y -12 = 0

Using the cross-multiplication method to solve these equations, we can find the point of intersection.

∆ = (3)(3) -(4)(-4) = 25

∆x = (-4)(-12) -(3)(0) = 48

∆y = (0)(4) -(-12)(3) = 36

(x, y) = (∆x/∆, ∆y/∆) = (48/25, 36/25)

(x, y) = (1.92, 1.44)

To read more about the cross-multiplication method, see

https://brainly.com/question/26397343

__

Additional comment

It is possible, but not easy, to read a value with 3 significant figures from a graph, unless the scale is specifically expanded to permit such precision. It is more likely that Sue would consider the point of intersection to be about (2, 1.5).