Which of the following rules represents the set of ordered pairs? {(2, 5), (3, 7), (5, 11),

a.ƒ(x ) = 2x + 1

b.ƒ(x ) = x + 5

c.ƒ(x ) = -x + 10

a

Step-by-step explanation:

To determine which ordered pair is a solution to the functions

Substitute the x- coordinate into the right side and if the value is equal to the y- coordinate then it is a solution.

(a) f(x) = 2x + 1

f(2) = (2 × 2) + 1 = 4 + 1 = 5 ⇒ (2,5) is a solution

f(3) = (2 × 3) + 1 = 6 + 1 = 7 ⇒ (3, 7) is a solution

f(5) = (2 × 5) + 1 = 10 + 1 = 11 ⇒ (5, 11) is a solution

(b) f(x) = x + 5

f(2) = 2 + 5 = 7 ⇒ (2, 5) is not a solution

f(3) = 3 + 5 = 8 ⇒ (3, 7) is not a solution

f(5) = 5 + 5 = 10 ⇒ (5, 11) is not a solution

(c) f(x) = - x + 10

f(2) = - 2 + 10 = 8 ⇒ (2, 5) is not a solution

f(3) = - 3 + 10 = 7 ⇒ (3, 7) is a solution

f(5) = - 5 + 10 = 5 ⇒ (5, 11) is not a solution

The only function representing the ordered pairs is (a)

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

10

step-by-step explanation: