Question

How is a system of equations created when each linear function is given as a set of two ordered pairs? Explain

Answer 1

Sample response: Use the two points of a linear function to write an equation in slope-intercept form by first finding the slope of the function, and then using a point and the slope to determine the y-intercept. Write the equations in slope-intercept form.

Answer 2

If each linear function is given as a set of two ordered pairs, you need to use those points to find the equation of each line, and then solve the system of equations.

For example:

Let's say that f(x) has the following ordered pais: (a, b) and (c, d) and g(x) has the following ordered pais: (e, f) and (g, h). We know that the general equation of a line is the following:

(y - yo) = m(x-xo), where 'm' represents the slope and (xo, yo) any point from the line.

The slope will be given by: (y1 - yo)/(x1 - x0).

For example, the equation of the line of f(x) is:

f(x) = (y - b) = [(d - b)/(c - a)](x-a)

You do the same for the function g(x), and then you are all set to solve the system of equations!