Q:

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

Accepted Solution

A:
Answer:Please check the explanation.Step-by-step explanation:If each linear function is given as a set of two ordered pairs, all we need is to find a slope between two lines and put one of the points in the slope- intercept form of the line equation to find the y-intercept 'b' and then writing the equation in the slope-intercept form. This is how we can generate a system of equations.For example, let suppose a linear function has the following ordered pairs:(1, 1) (2, 3)Finding the slope between two points[tex]\left(x_1,\:y_1\right)=\left(1,\:1\right),\:\left(x_2,\:y_2\right)=\left(2,\:3\right)[/tex][tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]m=\frac{3-1}{2-1}[/tex][tex]m=2[/tex]We know that the slope-intercept form of the line equation is[tex]y=mx+b[/tex]where m is the slope and b is the y-interceptNow, substituting the slope m = 2 and the point (1, 1) to determine the y-intercept[tex]y=mx+b[/tex][tex]1 = 2(1)+b[/tex][tex]b = 1-2[/tex][tex]b = -1[/tex]Now, substituting the slope m = 2 and the value of y-intercept in the slope-intercept form of the line equation[tex]y=mx+b[/tex][tex]y=2x+(-1)[/tex][tex]y=2x-1[/tex]Thus, the equation of a line with the linear function having the points (1, 1) and (2, 3) is:[tex]y=2x-1[/tex]This is how a system of equations created when each linear function is given as a set of two ordered pairs.