Answer:
183
Step-by-step explanation:
a₁ = -13
common difference = a₂ - a₁
= (-6) - (-13)
= -6 + 13
d = 7
nth term = a₁ + (n - 1)d
29th term = -13 + 28 * 7
= -13 + 196
= 183
Club A: 25+30x where x is the number of lesson
Club B 55 + 20x where x is the number of lesson
when is the cost equal
25+ 30x = 55 + 20x
subtract 20 x from each side
25+ 30x -20x = 55 - 20x
25+ 10x = 55
subtract 25 from each side
25-25+ 10x = 55 - 25
10 x = 30
divide by 10
10x/10 = 30/10
x = 3
After 3 lessons the cost is equal
To write the equation of a line, we need 1) a point on the line 2) it's slope
For the point, we just substitute in the equation of the line intersecting it with x=3 (because they share this point)
Therefore, 2*3-3y=6 --> That gives y=0
Then the point is (x1,y1)=(3,0)
We already have the slope : m=2
Now we should use this relation for the required line equation
(y-y1) / (x-x1) = m
Then (y-0) / (x-3) = 2
Then y = 2*x - 6
And that is the required form
where 2 is the slope and -6 is the intercept
