Which expression can be used to determine the number of people who can sit as a group if y tables are joined to form 1 long table? Justify in words why your answer is correct.
a) 4(y + 1)
b) 369 + 1)
c) 2(2y + 1)
d) 6y

c) 2(2y+1)

Step-by-step explanation:

This is because when the tables are together there can be 4 people at each table, plus 1 at either end. Whatever equation you have must have +2 in it, to account for the ends of the tables. The number of tables (y) must be multiplied by 4 because there are always 4 people per table. The number of tables is unknown so 4y must be in your equation.

2(2y+1) simplifies to 4y+2, which is the equation we want.

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