The line passes through the point (3,12)
and has the same slope as the line
y = 5x - 7.

           y - 12 = 5(x - 3)    {the point-slope form of the equation}

            y = 5x + 9            {the slope-intercept form of the equation}

           5x - y = -9            {standard form of the equation}

Step-by-step explanation:

The point-slope form of the equation is y - y₀ = m(x - x₀), where (x₀, y₀) is any point the line passes through and m is the slope:

y = 5x - 7     ⇒   m = 5

(3, 12)    ⇒   x₀ = 3,  y₀ = 12

So, the point-slope form of the equation:

y - 12 = 5(x - 3)

Therefore:

y - 12 = 5x - 3         {add 12 to both sides}

y = 5x + 9             ←  the slope-intercept form of the equation

y = 5x + 9               {subtract5x from both sides}

y - 5x = 9               {multiply both sides by (-1)}

5x - y = -9             ← the standard form of the equation

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺

step-by-step explanation: