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1 year ago

Which linear equation best represents the line of best fit for the scatterplot?

Mathematics

1 answer:

Lena [83]1 year ago

7 0

Answer:

$y = -\frac{1}{3}x$

Step-by-step explanation:

The scatter plot trends downward from left-> right, meaning that it is negative. Next, use two points to solve for the value for the slope.

In this case, I will use (-3 , 1) & (0 , 0)

Use the following equation. m = slope:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Let:

$(x_1 , y_1) = (0 , 0)\\(x_2 , y_2) = (-3 , 1)$

Plug in the corresponding numbers to the corresponding variables:

$m = \frac{1 - 0}{-3 - 0} = \frac{1}{-3} = -\frac{1}{3}$

Your answer will be:

$y = -\frac{1}{3}x$

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Part A

The height to which the projectile reaches is given by the following formula;

$\Delta y = y-y_0 = v_{0y} \times t-\dfrac{1}{2} \times g \times t^2$

Where;

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g = The acceleration due to gravity

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Given that the projectile has the same initial velocity, the variation of Δy with time, 't', will be the same when the project is launched from a different height, and the time change that it takes for the projectile to reach the maximum height will be the same for the previous launch height

Part B

From the change in eight of the projectile, Δy = y - y₀, the maximum height reached, 'y', is therefore given as follows;

y = Δy + y₀

The maximum height will increase by 'y₀', where 'y₀' is the difference between new height and the previous height, $y_i$

That is, if y₀ > $y_i$ , the maximum height reached increases and if y₀ < $y_i$ , y₀ will be added as y = Δy - y₀ and the maximum height reached decreases

Step-by-step explanation:

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