A straight line L is shown on the grid.
2 answers:
Answer:
y = 2x + 1
Step-by-step explanation:
Use slope-intercept form ( y = mx + b ) where m is the slope ( rise over run ) and the y-intercept is 1 because where x = 0, y =1. You can either use rise over run to solve the slope or plug in an x and y value on the line and solve algebriacally.
Rise Over Run:
Take two values on the line, for example, (0,1) and (1,3) y is the rise and x is the run, so write each one with y over x in fraction form.
(0,1) = (1,3) =
then subtract the second value from the first
-
=
which simplifies to 2. So the slope is 2.
Algebra:
plug a coordinate on the line into the equation y =mx + 1. For example (1,3)
3 = m(1) + 1 anything multiplied by 1 is itself so we can cancel out the 1 in the equation
3 = m + 1 subtract 1 from both sides
-1 -1
2 = m each method shows the slope is 2 so now we can put it together into the answer, y = 2x + 1
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Distance between two points, d, is given by
where: (x1, y1) = (2, 2) and (x2, y2) = (5, 5)
where: (x1, y1) = (2, 2) and (x2, y2) = (5, 5)
9514 1404 393
Answer:
n = 8
Step-by-step explanation:
"By inspection" is an appropriate method.
We are asked to compare the expressions
n·n
8·n
and find the value(s) of n that makes them equal. <em>By inspection</em>, we see that n=8 will make these expressions equal. We also know that both expressions will be zero when n=0.
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More formally, we could write ...
n^2 = 8n . . . . the two formulas give the same value
n^2 -8n = 0 . . . . rearrange to standard form
n(n -8) = 0 . . . . . factor
Using the zero product rule, we know the solutions will be the values of n that make the factors zero. Those values are ...
n = 0 . . . . . makes the factor n = 0
n = 8 . . . . . makes the factor (n-8) = 0
Generally, we're not interested in "trivial" solutions (n=0), so the only value of n that is of interest is n = 8.
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A lot of times, I find a graphing calculator to be a quick and easy way to find function argument values that make expressions equal.
