How do I write the rule for the nth term of the sequence -4, 8, -12, 16?
1 answer:
You might be interested in
Answer:
Step-by-step explanation:
x | y
-------
1 5
5 10
9 15
13 20
This one is linear because as x goes up by the same number so does y. So the ratio of difference of y to difference of x is the same per pair of points.
So a linear equation in slope-intercept form is y=mx+b where m is the slope and b is the y-intercept.
To find the slope, I'm going to line up the points vertically and subtract, then put 2nd difference over 1st difference. Like so,
( 1 , 5)
-( 5 , 10)
----------------
-4 -5
So the slope is 5/4 which makes sense since the y's are going up by 5 each time and the x's are going up by 4 each time.
So we have m=5/4. Let's plug that into our y=mx+b.
y=5/4 x+b
To find b, we need to use y=5/4 x+b along with one of the given points.
Choose; it doesn't matter. I like (1,5) I guess.
y=5/4 x +b with (1,5)
5=5/4 (1)+b
5=5/4 +b
Subtract 5/4 on both sides:
5-5/4=b
20/4-5/4=b (Found a common denominator)
15/4=b
The y-intercept is 15/4 so b=15/4.
So the equation for the line in slope-intercept form is y=5/4 x +15/4.