By the end of your 5th French lesson, you have learned 20 vocabulary words. After 10 lessons you know 40 vocabulary words. Write an equation that gives the number of vocabulary words you know, y, in the terms of the number of lessons you had, x.

Question

By the end of your 5th French lesson, you have learned 20 vocabulary words. After 10 lessons you know 40 vocabulary words. Write an equation that gives the number of vocabulary words you know, y, in the terms of the number of lessons you had, x.

Answer 1

Assuming that the learning of vocabulary words increases in a linear pattern, (it does not), you have two ordered pairs.

(5,20) and (10,40)

Just like you would in grade 9 geometry, find the slope, then use y = mx + b to find the equation.

Answer 2

Hello,

Did you try to answer yourself ?

x = number of lessons
y = number of vocabulary words

I help you : 5x = 20y ( 5th French lesson, you have learned 20 vocabulary words )

It's math

Good luck :)

Answer 3

slope = (40-20)/(10-5) = 4

so y = mx + b becomes
y = 4x + b
sub in (5,20)
20 = 4(5) + b
b = 0

so y = 4x is the equation.

Answer 4

To write an equation that relates the number of vocabulary words, y, to the number of lessons, x, we can identify the pattern in the given information.

According to the problem, the number of vocabulary words known increases by 20 after each set of 5 lessons.

From the information given, we can deduce that:
- After 5 lessons, you know 20 vocabulary words.
- After 10 lessons, you know 40 vocabulary words.

Since the number of vocabulary words increases by 20 after each set of 5 lessons, we can use a ratio to determine the pattern.

First, we calculate the rate of increase in vocabulary words per lesson:
Rate of increase = (Number of vocabulary words after 10 lessons - Number of vocabulary words after 5 lessons) / (Number of lessons after 10 lessons - Number of lessons after 5 lessons)
Rate of increase = (40 - 20) / (10 - 5)
Rate of increase = 20 / 5
Rate of increase = 4

Therefore, for every 5 lessons, the number of vocabulary words increases by 4.

Now, let's denote the number of vocabulary words after x lessons as y.

From the pattern we discovered, we can express the equation as follows:
y = 20 + 4(x - 5)

Explanation of the equation:
- We start with 20 since that is the number of vocabulary words after 5 lessons.
- We add the rate of increase (4) times the number of additional lessons beyond the initial 5 lessons (x - 5).

This equation allows you to determine the number of vocabulary words, y, in terms of the number of lessons, x.