Question

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

Answer 1

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

$\left(x_1,\:y_1\right)=\left(1,\:1\right),\:\left(x_2,\:y_2\right)=\left(2,\:3\right)$

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{3-1}{2-1}$

$m=2$

We know that the slope-intercept form of the line equation is

$y=mx+b$

where m is the slope and b is the y-intercept

Now, substituting the slope m = 2 and the point (1, 1) to determine the y-intercept

$y=mx+b$

$1 = 2(1)+b$

$b = 1-2$

$b = -1$

Now, substituting the slope m = 2 and the value of y-intercept in the slope-intercept form of the line equation

$y=mx+b$

$y=2x+(-1)$

$y=2x-1$

Thus, the equation of a line with the linear function having the points (1, 1) and (2, 3) is:

• $y=2x-1$

This is how a system of equations created when each linear function is given as a set of two ordered pairs.

Answer 2

Answer:

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.