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2 years ago

How would I graph a line that contains the point (6,5) and has a slope of - 2/3 ?

Mathematics

2 answers:

ddd [48]2 years ago

6 0

Answer:

y=-2/3x+9

Step-by-step explanation:

Use point-slope formula:

y-y1 = m(x-x1)

y-5=-2/3(x-6)

y-5=-2/3x+4

y=-2/3x+9

You would then proceed to graphing this equation, as it is in slope intercept form now.

HTH :)

Semenov [28]2 years ago

6 0

Y=-2/3x+5
Answer is

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LUCKY_DIMON [66]

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the equation of circle is given by

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2 years ago

Two lighthouses are located 75 miles from one another on a north-south line. If a boat is spotted S 40o E from the northern ligh

yuradex [85]

Answer:

The northern lighthouse is approximately $24.4\; \rm mi$ closer to the boat than the southern lighthouse.

Step-by-step explanation:

Refer to the diagram attached. Denote the northern lighthouse as $\rm N$ , the southern lighthouse as $\rm S$ , and the boat as $\rm B$ . These three points would form a triangle.

It is given that two of the angles of this triangle measure $40^{\circ}$ (northern lighthouse, $\angle {\rm N}$ ) and $21^{\circ}$ (southern lighthouse $\angle {\rm S}$ ), respectively. The three angles of any triangle add up to $180^{\circ}$ . Therefore, the third angle of this triangle would measure $180^{\circ} - (40^{\circ} + 21^{\circ}) = 119^{\circ}$ (boat $\angle {\rm B}$ .)

It is also given that the length between the two lighthouses (length of $\rm NS$ ) is $75\; \rm mi$ .

By the law of sine, the length of a side in a given triangle would be proportional to the angle opposite to that side. For example, in the triangle in this question, $\angle {\rm B}$ is opposite to side $\rm NS$ , whereas $\angle {\rm S}$ is opposite to side ${\rm NB}$ . Therefore:

$\begin{aligned} \frac{\text{length of NS}}{\sin(\angle {\rm B})} = \frac{\text{length of NB}}{\sin(\angle {\rm S})} \end{aligned}$ .

Substitute in the known measurements:

$\begin{aligned} \frac{75\; \rm mi}{\sin(119^{\circ})} = \frac{\text{length of NB}}{\sin(21^{\circ})} \end{aligned}$ .

Rearrange and solve for the length of $\rm NB$ :

$\begin{aligned} & \text{length of NB} \\ =\; & (75\; \rm mi) \times \frac{\sin(21^{\circ})}{\sin(119^{\circ})} \\ \approx\; & 30.73\; \rm mi\end{aligned}$ .

(Round to at least one more decimal places than the values in the choices.)

Likewise, with $\angle {\rm N}$ is opposite to side ${\rm SB}$ , the following would also hold:

$\begin{aligned} \frac{\text{length of NS}}{\sin(\angle {\rm B})} = \frac{\text{length of SB}}{\sin(\angle {\rm N})} \end{aligned}$ .

$\begin{aligned} \frac{75\; \rm mi}{\sin(119^{\circ})} = \frac{\text{length of SB}}{\sin(40^{\circ})} \end{aligned}$ .

$\begin{aligned} & \text{length of SB} \\ =\; & (75\; \rm mi) \times \frac{\sin(40^{\circ})}{\sin(119^{\circ})} \\ \approx\; & 55.12\; \rm mi\end{aligned}$ .

In other words, the distance between the northern lighthouse and the boat is approximately $30.73\; \rm mi$ , whereas the distance between the southern lighthouse and the boat is approximately $55.12\; \rm mi$ . Hence the conclusion.

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2 years ago

Please HELP ME ON THIS MATH WRITTEN RESPONSE QUESTION.. THANK YOU

sergij07 [2.7K]

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Step-by-step explanation:

Point A is (-4,6)

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Point D is (13,-1)

Given that the diagonals of a square are perpendicular to each other;

We know that the product of slopes of two perpendicular lines is -1.

So, slope(m) of AC × slope(m) of BD should be equal to -1.

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Slope of BD = (Change in y-axis) ÷ (Change in x-axis) = (-1 - -12) ÷ (13 - -12) = 11/25 = 0.44

The product of slope of AC and slope of BD = -2.4 × 0.44 = -1.056

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3 years ago

How would I graph a line that contains the point (6,5) and has a slope of - 2/3 ?​

How would I graph a line that contains the point (6,5) and has a slope of - 2/3 ?