Type an equation for the following pattern x: 1 | 2 | 3 | 4 | 5 y: 1 | 4 | 9 | 16 | 25

y = x²

Explanation:

x    |    y

1     |    1    

2    |    4    

3    |    9

4    |    16

5    |    25

The x-coordinates increase by 1 unit.  Now, look at the intervals of the y-coordinates:

1 to 4 = 3

4 to 9 = 5

9 to 16 = 7

16 to 25 = 9

Their intervals are not equal so it is not a linear equation (y = x). So, go one more generation and compare the intervals above:

3 to 5 = 2

5 to 7 = 2

7 to 9 = 2

Their intervals are equal so it is a quadratic equation (y = x²).

Note: First generation is a linear equation.

         Second generation is a quadratic equation.

i think it is c, not positive though

step-by-step explanation:

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