A function is initially defined by the set of coordinate pairs ((-3,7), (1,5), (4,13)). Which coordinate pair below, if added to this set, prevents the set from representing a function? 1) (2,5) 2) (5,0) 3) (-1,8) 4) (1,4)

We conclude that if we add (1, 4) to this set, it prevents the set from representing a function.

Step-by-step explanation:

Given the initial function

{(-3, 7), (1, 5), (4, 13)}

We know that the given function indicates the relation in which each input has only one output.

i.e.

at x = -3, y = 7

at x = 1, y = 5

at x = 4,y = 13

Thus, it represents a function, becaus there is no repetitive inputs.

The only way the above function will no longer be a function we bring a point, adding of which makes the initial function having repetitive inputs.

i.e. if we add (1, 4) to the initial set, the relation will no longer be a function.

because induction of the point (1, 4) causes repetitive inputs because x = 1 is already present in the set.

so adding the point (1, 4)

{(-3, 7), (1, 4), (1, 5), (4, 13)}

Now, check the points (1, 4) and (1, 5).

It is clear that there are multiple outputs for x = 1. In other words, the input is no more a unique value as x=1 has been repeated multiple times.

Therefore, we conclude that if we add (1, 4) to this set, it prevents the set from representing a function.

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form