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2 years ago

Line M contains the following two points: (1, 10) and (6, 20). What is the slope of line M?

Mathematics

1 answer:

iren2701 [21]2 years ago

3 0

Answer:

The slope is 2.

Step-by-step explanation:

In order to find the slope of the line, we need to start by using the points in the slope formula.

m(slope) = (y2 - y1)/(x2 - x1)

m = (20 - 10)/(6 - 1)

m = 10/5

m = 2

So the slope of this line would be 2

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One of the x-intercepts of the parabola represented by the equation y = 3x^2 + 6x − 10 is approximately (1.08, 0).

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2 years ago

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3 years ago

Find the equation of the locus of a point that moves so that its distance from the line 12x-5y-1=0 is always 1 unit.

leonid [27]

<u>Answer-</u>

The equations of the locus of a point that moves so that its distance from the line 12x-5y-1=0 is always 1 unit are

$12x-5y+14=0 \\ 12x-5y-14=0$

<u>Solution-</u>

Let a point which is 1 unit away from the line 12x-5y-1=0 is (h, k)

The applying the distance formula,

$\Rightarrow \left | \frac{12h-5k-1}{\sqrt{12^2+5^2}} \right |=1$

$\Rightarrow \left | \frac{12h-5k-1}{\sqrt{169}} \right |=1$

$\Rightarrow \left | \frac{12h-5k-1}{13} \right |=1$

$\Rightarrow 12h-5k-1=\pm 13$

$\Rightarrow 12h-5k=\pm 14$

$\Rightarrow 12h-5k=14,\ 12h-5k=-14$

$\Rightarrow 12h-5k-14=0,\ 12h-5k+14=0$

$\Rightarrow 12x-5y-14=0,\ 12x-5y+14=0$

Two equations are formed because one will be upper from the the given line and other will be below it.

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2 years ago