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hoa [83]
3 years ago
12

What is the slope, y-intercept, and linear function?

Mathematics
2 answers:
victus00 [196]3 years ago
4 0

Answer:

slope = - 1/3

y-intercept = (0, 5)

point-slope form = y - 4 = -1/3 x (x - 3)

Step-by-step explanation:

sp2606 [1]3 years ago
3 0

Answer:

Slope: -\frac{1}{3}

y-intercept: (0, 5)

Linear function: y = -\frac{1}{3}x + 5

Step-by-step explanation:

To find the slope, use this formula: \frac{y2-y1}{x2-x1} (you need 2 points)

I'll use (0, 5) and (3, 4):

\frac{4-5}{3-0} = -\frac{1}{3}

Recall that the y-intercept is the point that lies on the y-axis of the function (in that point, the x-coordinate is 0). When looking at the graph, the only point at which the line intersects the y-axis is (0, 5), so that is your y-intercept. At that point, the x-coordinate is 0.

I'm not sure if the question wants you to put the equation for the linear function in slope-intercept form, but I'm assuming it does since it asked you for the slope and y-intercept. So, to find the equation in slope-intercept form, first recall that slope-intercept form is y = mx + b, where m is the slope and b is your y-intercept. At that point, just plug in your values to get y = -\frac{1}{3}x + 5

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  1. Raising a power to a power: (x^m)^n=x^{m*n}
  2. Dividing exponents of the same base: \frac{x^m}{x^n}=x^{m-n}
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Firstly, solve the outer exponent:

(\frac{4mn}{m^{-2}n^{6}})^{-2}=\frac{4^{-2}m^{-2}n^{-2}}{m^{-2*-2}n^{6*-2}}=\frac{4^{-2}m^{-2}n^{-2}}{m^4n^{-12}}

Next, divide:

\frac{4^{-2}m^{-2}n^{-2}}{m^4n^{-12}}=4^{-2}m^{-2-4}n^{-2-(-12)}=4^{-2}m^{-6}n^{10}

Next, convert the negative exponents:

4^{-2}m^{-6}n^{10}=\frac{n^{10}}{4^2m^6}=\frac{n^{10}}{16m^6}

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