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3 years ago

Write an equation in the form y = mx + b that represents this line.

Mathematics

1 answer:

kondaur [170]3 years ago

8 0

Answer:

Step-by-step explanation:

The form, y = mx + b is the slope intercept form of a straight line.

Where b = intercept

m = slope = (change in the value of y in the vertical axis) / (change in the value of x in the horizontal axis.

Slope = (y2 - y1)/(x2 - x1)

y2 represents final value of y = - 3

y1 represents initial value of y = 3

x2 represents final value of x = 3

x1 represents initial value of x = 0

Therefore,

slope = (- 3 - 3)/(3 - 0) = - 6/3 = - 2

To determine the intercept, we would substitute m = - 2, x = 3 and y = -3 into y = mx + b. It becomes

- 3 = - 2 × 3 + b = - 6 + b

b = - 3 + 6 = 3

The equation becomes

y = - 3x + 3

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$\implies \displaystyle 5 \int_0^1 (3t-2) e^{4t} \,dt = \frac54 (3t-2) e^{4t} \bigg|_{t=0}^{t=1} - \frac{15}4 \int_0^1 e^{4t} \,dt \\\\ ~~~~~~~~ = \frac54 (e^4 + 2) - \frac{15}{16} e^{4t} \bigg|_{t=0}^{t=1} \\\\ ~~~~~~~~ = \frac54 (e^4 + 2) - \frac{15}{16} (e^4 - 1) = \boxed{\frac{5e^4 + 55}{16}}$

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