What is the equation of the line graphed below?

Mathematics

2 answers:

Verdich [7]3 years ago

8 0

1/2x + y = 3

Solve the equation to put it in slope intercept form. (y=mx+b)

1/2x + y = 3

Subtract 1/2x from both sides.

y = -1/2x + 3

The y-intercept (where the line crosses the y-axis) is three and the slope (rise over run) is -1/2.

Hope this helps!

tangare [24]3 years ago

3 0

Answer: A. $\dfrac{1}{2}x+y=3$

Step-by-step explanation:

The equation of a line passing through two points (a,b) and (c,d) is given by :-

$(y-b)=\dfrac{d-b}{c-a}(x-a)$

Then the equation of a line passing through two points (0,3) and (6,0) is given by :-

$(y-3)=\dfrac{0-3}{6-0}(x-0)\\\\\Rightarrow\ y-3=\dfrac{-1}{2}x\\\\\Rightarrow\ \dfrac{1}{2}x+y=3$

Hence, the equation which is graphed in the given picture :-

$\dfrac{1}{2}x+y=3$

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A food packet is dropped from a helicopter and is modeled by the function f(x) = −15x2 + 6000. The graph below shows the height

melisa1 [442]

General Idea:

Domain of a function means the values of x which will give a DEFINED output for the function.

Applying the concept:

Given that the x represent the time in seconds, f(x) represent the height of food packet.

Time cannot be a negative value, so

$x\geq 0$

The height of the food packet cannot be a negative value, so

$f(x)\geq 0$

We need to replace $-15x^2+6000$ for f(x) in the above inequality to find the domain.

$-15x^2+6000\geq 0 \; \; [Divide \; by\; -15\; on\; both\; sides]\\ \\ \frac{-15x^2}{-15} +\frac{6000}{-15} \leq \frac{0}{-15} \\ \\ x^2-400\leq 0\;[Factoring\;on\;left\;side]\\ \\ (x+200)(x-200)\leq 0$

The possible solutions of the above inequality are given by the intervals $(-\infty , -2], [-2,2], [2,\infty )$ . We need to pick test point from each possible solution interval and check whether that test point make the inequality $(x+200)(x-200)\leq 0$ true. Only the test point from the solution interval [-200, 200] make the inequality true.