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3 years ago

Two linear functions are displayed. Function One is represented by the graph:

Mathematics

2 answers:

GarryVolchara [31]3 years ago

3 0

Answer:

Option A

Step-by-step explanation:

Function One is represented by the graph. We can see that the slope of the First Function is positive because the formula of slope is

$Slope=\frac{Change\ in\ y}{Change\ in\ x} \\\\$

And we can see that in the graph the change in y and change in x are both positive as the function is increasing because if we see the graph closely,

When x = 1 the value of y = 2 and when x = 2 the value of y = 4 and when x = 3 the value of y = 6 so the values are increasing of x and of y hence the slope is positive and the value of slope is 2.

Now the Second Function which is y = -4x here the slope is negative because the slope-intercept form of the equation is .

$y=mx+b$

and the second function is

$y=-4x$

if we compare both these equations we get the value of m = -4 where m is also called the slope. So the slope of the second function is negative.

Option B is incorrect because the slope of the first function is positive

Option C is incorrect because the slope of the second function is negative

Option D is incorrect because the slope of the first function is 2 and the slope of the second function is -4

That leaves us with Option A which is correct, where we can see that the slope of the first function is positive and the slope of the second function is negative

vredina [299]3 years ago

3 0

Answer:

A) The slope of function one is positive and the slope of function two is negative.

General Formulas and Concepts:

Algebra I

Slope-Intercept Form: y = mx + b

m - slope
b - y-intercept

Step-by-step explanation:

We see that the 1st graph has a positive slope; as x increases, the y-value also increases. Therefore, the 1st graph must have a positive slope.

We are given the equation y = -4x as our second line. Using our y = mx + b form, we see that our slope m = -4. Therefore, the 2nd graph has a negative slope.

Our answer choice then would be A, as it is the only one that matches the descriptions.

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Step-by-step explanation:

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$\displaystyle\frac{\text{Displacement}}{\text{Time}}$

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$y(1 + 0.01)=y(1.01) = 43(1.01)-23(1.01)^{2} = 19.9677\\\\\text{Average Velocity} = \dfrac{y(1.01)-y(1)}{1.01-1} =\dfrac{19.9677-20}{1.01-1}= \dfrac{-0.0323}{0.01} = -3.230000 \text{feet per second}$

2) 0.005 s

$y(1 + 0.005)=y(1.005) = 43(1.005)-23(1.005)^{2} = 19.984425\\\\\text{Average Velocity} = \dfrac{y(1.005)-y(1)}{1.005-1} =\dfrac{19.984425-20}{1.005-1} = -3.1150000 \text{feet per second}$

3) 0.002 s

$y(1 + 0.002)=y(1.002) = 43(1.002)-23(1.002)^{2} = 19.993908\\\\\text{Average Velocity} = \dfrac{y(1.002)-y(1)}{1.002-1} =\dfrac{19.993908-20}{1.002-1} = -3.0460000 \text{feet per second}$

4) 0.001 s

$y(1 + 0.001)=y(1.001) = 43(1.001)-23(1.001)^{2} = 19.996977\\\\\text{Average Velocity} = \dfrac{y(1.001)-y(1)}{1.001-1} =\frac{19.996977-20}{1.001-1} = -3.0230000 \text{feet per second}$

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