1) You learn 15 vocabulary words a week & ahve already learned 75. Type an equation for the total vocabulary words you will learn in x week. 2) Find the slope
3) How many new vocabulary words do you learn in 13 weeks?
4) How many weeks will it take you to learn 390 vocabulary words?

1) Words learned=15x+75

2) 15 is the slope

3) 270 words

4) 21 weeks

Step-by-step explanation:

Let x be equal to the number of weeks that pass.

Let y be equal to the number of words we learn.

1) We're told that we learn 15 words per week. Therefore, 15x would equal the number of words we learn. However, because we already know 75, we add that to 15x, giving us this equation:

y=15x+75

2) The slope is the same thing as the rate of change in a situation. In this scenario, every week, we learn 15 words. Therefore, the rate of change, or the slope, is 15.

3) To find this, plug 13 into our equation as x and solve for y.

y=15x+75

y=15(13)+75

y=195+75

y=270

Therefore, we would learn 270 vocabulary words in total in 13 weeks.

4) To find this, plug 390 into our equation as y and solve for x.

y=15x+75

390=15x+75

Subtract 75 on both sides to isolate x

390-75=15x+75-75

315=15x

Divide both sides by 15

315/15=15x/15

21=x

Therefore, it would take 21 weeks to learn 390 new vocabulary words.

I hope this helps!

because linear equations are a lot simpler than quadratics equations, and linear equations formula is a lot easier to memorize. that's why i think they're harder.