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3 years ago

Point R(5,-3) and point N(9,-4) are on line k. What is the slope of the line passing through these points?

1 answer:

8 0

The slope of a line, denoted "m" is:

m=(y2-y1)/(x2-x1), where (x1,y1) and (x2,y2) are any two points on the line.

m=(-4--3)/(9-5)

m=-1/4

So the slope is negative one quarter.

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Nonamiya [84]

Answer:

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Step-by-step explanation:

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3 years ago

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Draw the image of the following segment after a dilation centered at the origin with a scale factor of 2/3

Irina18 [472]

Answer:

Step-by-step explanation:

Let the ends of the given segment are A and B.

Coordinates of A → (8, 6)

Coordinates of B → (12, 12)

If a point (x, y) is dilated by a scale factor 'k' about the origin, rule to be followed,

(x, y) → (kx, ky)

If k = $\frac{2}{3}$

(x, y) → $(\frac{2}{3}x, \frac{2}{3}y)$

By this rule coordinates of the image points of A and B will be,

A(8, 6) → $A'(\frac{2\times 8}{3},\frac{2\times 6}{3})$

→ A'(5.3, 4)

B(12, 12) → $B'(\frac{12\times 2}{3}, \frac{12\times 2}{3})$

→ B'(8, 8)

Now we can get the image of segment AB after dilation by a scale factor of $\frac{2}{3}$ .

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3 years ago

Find all constants a such that the vectors (a, 4) and (2, 5) are parallel.

Nezavi [6.7K]

Answer:

$\displaystyle a = \frac{8}{5}$ .

Step-by-step explanation:

Two vectors $(x_1,\, y_1)$ and $(x_2,\, y_2)$ are parallel to one another if and only if the ratio between their corresponding components are equal:

$\displaystyle \frac{x_1}{x_2} = \frac{y_1}{y_2}$ .

Equivalently:

$\displaystyle \frac{x_1}{y_1} = \frac{x_2}{y_2}$ .

For the two vectors in this equation to be parallel to one another:

$\displaystyle \frac{a}{4} = \frac{2}{5}$ .

Solve for $a$ :

$\displaystyle a = \frac{8}{5}$ .

$\displaystyle \frac{8}{5}$ would be the only valid value of $a$ ; no other value would satisfy the $\displaystyle \frac{x_1}{y_1} = \frac{x_2}{y_2}$ equation.

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3 years ago

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Sedaia [141]

Answer:

Step-by-step explanation:

because thats the answer

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3 years ago

Find an equation of the line containing the given pair of points (4,1) and (12,7)

Eva8 [605]

Answer:

Y = 3/4 X -2

Step-by-step explanation:

Just apply the equation of a straight line (Y=mX+C), remembering that m represents the gradient of the line. This can be found by dividing the change in the y-axis by the change in the x-axis. Then substitute a set of coordinates with your obtained gradient into Y=mX+C to obtain C, i.e. the y-intercept.

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3 years ago