Question

Is g = {(1, 1), (2, 3), (3, 5), (4, 7)} a function? Justify. If this is described by the
relation, g (x) = αx + β, then what values should be assigned to α and β?

Answer 1

One of the most important properties of a straight line is in how it angles away from the horizontal.

This concept is reflected in something called the "slope" of the line

For straight lines, slope is constant (always the same).

You can graph the points and "count" the vertical changes and horizontal changes to use in the formula:

á = slope = Vertical change / horizontal change

á = slope = [ g (n) - g ( n-1 ) ] / [ x (n) - x ( n-1 )

In this case :

á = [ g (2) - g ( 1 ) ] / [ x (2) - x ( 1 ) = ( 3 - 1 ) / ( 2 - 1 ) = 2 / 1 = 2


á = [ g (3) - g ( 2 ) ] / [ x (3) - x ( 2 ) = ( 5 - 3 ) / ( 3 - 2 ) = 2 / 1 = 2


á = [ g (4) - g (3 ) ] / [ x (4) - x ( 3 ) = ( 7 - 5 ) / ( 4 - 3 ) = 2 / 1 = 2


á = slope = 2


When you know á you can put any point in your equation. For example x = 3 , g = 5

g (x) = áx + â

5 = 2 * 3 + â

5 = 6 + â Subtract 6 to both sides

5 - 6 = 6 + â - 6

- 1 = â

â = - 1


g (x) = áx + â

g (x) = 2x - 1

Answer 2

á = Greek letter alpha

â = Greek letter beta