6x + 2y = 24....subtract 6x from both sides
2y = -6x + 24...now divide both sides by 2
y = -6/2x + 24/2...now reduce
y = -3x + 12 <=== slope intercept form of y = mx + b
Given Ratio
-------------------
16 : 4
16 ÷ 4 : 4 ÷ 4 ← Divide by 4 on both sides
4 : 1
------------------------------------------------------------------------
Answer: Yes, 16: 4 and 4: 1 are proportional.
------------------------------------------------------------------------
Answer:
f(n) = - 0.5n + 6
Step-by-step explanation:
Because Vince cuts down his television watching at a steady pace, his situation models a linear function. As such, we can use slope-intercept form to write and predict his hours watching tv in n weeks.
Slope-intercept form is y=mx+b. In this case, we are choosing to use f(n) instead of y to show the number of hours he is watching tv. We are also choosing to use n weeks instead of x. So we have the form f(n)=mn+b.
We know that Vince starts out at watching 6 hours a week. This is our initial value known as the y-intercept and represented by b. As each week passes, he will decrease from the previous week by 30 minutes or -0.5 hours since 30 out of 60 minutes is 0.5. And since he is decreasing it should be a negative rate of -0.5 and is represented by m.
We substitute b=6 and m=0.5 into our form to get f(n)=-0.5n+6. Let's test week 1. After 1 week he should be down from 6 hours to 5.5 hours or 5 hours and 30 minutes. Let's substitute n=1.
f(n)=-0.5(1)+6=-0.5+6=5.5
We can substitute for any n week and find the amount.
Answer: x=7
Step-by-step explanation:
(5x-40)+7 = 2
5x-33 = 2
5x = 35
x = 35/5
x = 7
