The following set of real numbers R = { (x,y) : (2,3), (4,4), (6,5), (8,6)...} is linear.
<h3>What is a set ?</h3>
A set is a collection of well defined objects.
According the given set we have R = { (x,y) : (2,3), (4,4), (6,5), (8,6)...}
The set is of real numbers and it is linear.We can define this linear relationship by for every 2 point right shift or run in x axis results in 1 point up shift in y axis or rise.
We know linear equation is of form y = mx + b. Where m is the slope and b is the y intercept.
Slope(m) = rise/run or (y₂ - y₁)/(x₂ - x₁).
lets take two pair of co-ordinates from he given set.
(x₁,y₁) = (2,3) and (y₁,y₂) = (4,4).
Slope (m) = (4 - 2)/(4 -3)
m = 2.
Now the equation can be written as
y = 2x + b to find the y intercept we will put the values of x and y from any of the co-ordinate.
(x,y) = (2,3)
∴ y = mx + b
3 = 2(2) + b
b = -1.
∴ y = 2x - 1.
learn more about sets here :
brainly.com/question/8053622
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