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3 years ago

Write various of the equation of a line that passes through (-6, 3) and has a slope of - 1/3

Mathematics

1 answer:

pishuonlain [190]3 years ago

5 0

Answer:

$\large\boxed{y-3=-\dfrac{1}{3}(x+6)-\text{point-slope form}}\\\boxed{y=-\dfrac{1}{3}x+1-\text{slope-intercept form}}\\\boxed{x+3y=3-\text{standard form}}$

Step-by-step explanation:

The point-slope form of an equation of a line:

$y-y_1=m(x-x_1)$

m - slope

We have

$m=-\dfrac{1}{3},\ (-6,\ 3)\to x_1=-6,\ y_1=3$

Substitute:

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

Convert to the slope-intercept form

$y=mx+b$

$y-3=-\dfrac{1}{3}(x+6)$ use the distributive property

$y-3=-\dfrac{1}{3}x-2$ add 3 to both sides

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

Convert to the standard form

$Ax+By=C$

$y=-\dfrac{1}{3}x+1$ multiply both sides by 3

$3y=-x+3$ add x to both sides

$x+3y=3$

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3 years ago

20% of the students in the class play an instrument. if there are 35 students in class, how many play an instrument?

kondor19780726 [428]

Answer:

7 students play an instrument.

Calculation:

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2 years ago

A piano teacher has 4 1/2 hours available to teach in a night. Each lesson will last 1 1/2 hours. How many lessons can the teach

kherson [118]

Answer:

3 classes

Step-by-step explanation:

The teacher can schedule 3 classes in a night because 4 1/2 divided by 1 1/2 is 3.

hope this helps!!

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3 years ago

Read 2 more answers

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djyliett [7]

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2 years ago

The number of salmon swimming upstream to spawn is approximated by the following function:

umka2103 [35]

Answer:

The water temperature that produces the maximum number of salmon swimming upstream is approximately 12.305 degrees Celsius.

Step-by-step explanation:

Let $S(x) = -x^{3}+2\cdot x^{2}+405\cdot x +4965$ , for $6 \leq x \leq 20$ . $x$ represents the temperature of the water, measured in degrees Celsius, and $S$ is the number of salmon swimming upstream to spawn, dimensionless.

We compute the first and second derivatives of the function:

$S'(x) = -3\cdot x^{2}+4\cdot x +405$ (Eq. 1)

$S''(x) = -6\cdot x +4$ (Eq. 2)

Then we equalize (Eq. 1) to zero and solve for $x$ :

$-3\cdot x^{2}+4\cdot x +405 = 0$

And all roots are found by Quadratic Formula:

$x_{1} \approx 12.305\,^{\circ}C$ , $x_{2}\approx -10.971\,^{\circ}C$

Only the first root is inside the given interval of the function. Hence, the correct answer is:

$x \approx 12.305\,^{\circ}C$

Now we evaluate the second derivative at given result. That is:

$S''(12.305) = -6\cdot (12.305)+4$

$S''(12.305) = -69.83$

According to the Second Derivative Test, a negative value means that critical value leads to a maximum. In consequence, the water temperature that produces the maximum number of salmon swimming upstream is approximately 12.305 degrees Celsius.

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3 years ago