What is the equation of the line in slope intercept form write your answer using integers, proper fractions, and improper tracti
ons in simplest form
1 answer:
Answer:
y = 2x - 1
Step-by-step explanation:
To find out the equation of the line, you will <u>always</u> need the following information in order to determine the linear equation in slope-intercept form, y = mx + b:
1. 2 sets of ordered pairs (x, y)
2. Slope (m)
3. Y-intercept (b)
First, we need to choose 2 points from the graph to solve for the slope:
Let (x1, y1) = (0, -1)
(x2, y2) = (3, 5)
Substitute these values into the following slope formula:
Therefore, the slope (m) = 2.
Next, we need the y-intercept, (b). The y-intercept is the y-coordinate of the point where the graph of the linear equation crosses the y-axis. The y-intercept is also the value of y when x = 0. The y-coordinate of the point (0, -1) is the y-intercept. Hence, the y-intercept (b) = -1.
Given our slope, m = 2, and the y-intercept (b) = -1, the linear equation is:
y = 2x - 1
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Answer:
31
Step-by-step explanation:
The series are given as geometric series because these terms have common ratio and not common difference.
Our common ratio is 2 because:
1*2 = 2
2*2 = 4
The summation formula for geometric series (r ≠ 1) is:
or
You may use either one of these formulas but I’ll use the first formula.
We are also given that n = 5, meaning we are adding up 5 terms in the series, substitute n = 5 in along with r = 2 and first term = 1.
Therefore, the solution is 31.
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Summary
If the sequence has common ratio then the sequence or series is classified as geometric sequence/series.
Common Ratio can be found by either multiplying terms with common ratio to get the exact next sequence which can be expressed as meaning “previous term times ratio = next term” or you can also get the next term to divide with previous term which can be expressed as:
Once knowing which sequence or series is it, apply an appropriate formula for the series. For geometric series, apply the following three formulas:
Above should be applied for series that have common ratio not equal to 1.
Above should be applied for series that have common ratio exactly equal to 1.
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Topics
Sequence & Series — Geometric Series
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Others
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The smallest natural number is 1. The largest natural number does not exists because there will always be one even larger. But if you are asking the number of all natural numbers or the size of natural number set then is your answer.