by the end of your 6th Spanish lesson you have learned 20 vocabulary words. when you started (0 lessons) you only knew 2 words. write an equation that gives the number of vocabulary words you know, y, in terms of the number of lessons you have had, x. (iv tried many things but i just don't know how to do this problem)
y = 2 + (20-2)/6 x = 2+3x
This comes about because in 6 lessons you have learned 18 words. That's 3 words/lesson, starting with 2.
To solve this problem, let's break it down step by step:
1. We know that at the beginning (0 lessons), you only knew 2 words. This can be represented as the initial value of vocabulary words, y₀ = 2.
2. By the end of the 6th lesson, you have learned 20 vocabulary words. This provides us with another data point, which can be represented as y₆ = 20.
3. We need to come up with an equation that relates the number of lessons, x, to the number of vocabulary words, y. Since we are given two data points (x = 0, y = 2) and (x = 6, y = 20), we can form a linear equation in the form of y = mx + c, where m is the slope and c is the y-intercept.
4. To find the slope, we can use the formula:
slope (m) = (change in y)/(change in x) = (y₂ - y₁)/(x₂ - x₁)
Plugging in the values of (x₁, y₁) = (0, 2) and (x₂, y₂) = (6, 20), we get:
m = (20 - 2)/(6 - 0) = 18/6 = 3
5. Now that we have the slope (m), we can substitute it into the equation:
y = mx + c
y = 3x + c
Since we have a specific point (x = 0, y = 2), we can substitute these values to solve for c:
2 = 3(0) + c
2 = c
6. With the value of c, we can now write the final equation:
y = 3x + 2
Thus, the equation that gives the number of vocabulary words you know (y) in terms of the number of lessons you have had (x) is y = 3x + 2.