Answer:
D. 7 units.
Step-by-step explanation:
The length is not altered by the 2 translations.
It is √[ (-1-6)^2 + (2-2)^2]
= 7 units.
i think it’s is a for the first one
To find the slope, you should rearrange the equation into slope-intercept form, ie. y = mx + c, where m is the gradient.
y - 9 = 15(x - 5)
y = 15(x - 5) + 9 (Add 9 to each side)
y = 15x - 15*5 + 9 (Expand 15(x - 5))
y = 15x - 75 + 9
y = 15x - 66
Therefor, the slope of the equation is 15.
The vertex is the high point of the curve, (2, 1). The vertex form of the equation for a parabola is
.. y = a*(x -h)^2 +k . . . . . . . for vertex = (h, k)
Using the vertex coordinates we read from the graph, the equation is
.. y = a*(x -2)^2 +1
We need to find the value of "a". We can do that by using any (x, y) value that we know (other than the vertex), for example (1, 0).
.. 0 = a*(1 -2)^2 +1
.. 0 = a*1 +1
.. -1 = a
Now we know the equation is
.. y = -(x -2)^2 +1
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If we like, we can expand it to
.. y = -(x^2 -4x +4) +1
.. y = -x^2 +4x -3
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An alternative approach would be to make use of the zeros. You can read the x-intercepts from the graph as x=1 and x=3. Then you can write the equation as
.. y = a*(x -1)*(x -3)
Once again, you need to find the value of "a" using some other point on the graph. The vertex (x, y) = (2, 1) is one such point. Subsituting those values, we get
.. 1 = a*(2 -1)*(2 -3) = a*1*-1 = -a
.. -1 = a
Then the equation of the graph can be written as
.. y = -(x -1)(x -3)
In expanded form, this is
.. y = -(x^2 -4x +3)
.. y = -x^2 +4x -3 . . . . . . same as above
The answer is -2. The line is going from left to right which makes it negative. Then if you look at the line and do change in y(rise) over change in x(run).
