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3 years ago

Which is an equation for the line with a slope of 1/3, and passes through the point (–2, 1)?

Mathematics

1 answer:

worty [1.4K]3 years ago

8 0

Answer:

y = (1/3)x +5/3

Step-by-step explanation:

The general equation of a line is

y = mx+b

where m is the slope and b the y-intercept

Since the slope is 1/3 we have

y = (1/3)x +b

since the line passes through (x,y) = (-2,1) this point satisfies the equation

1 = (1/3)(-2) + b ===> b = 1+2/3 ===> b = 5/3

and the equation of the line is

y = (1/3)x +5/3

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A 30° 60° 90° triangle is shown below. Find the length of the side labeled y.

bulgar [2K]

Answer:

Part 1) $y=3\ units$

Part 2) The length of the hypotenuse is 6 units

Step-by-step explanation:

Part 1) we know that

In the right triangle of the figure

$sin(60^o)=\frac{y}{2\sqrt{3}}$ ----> by SOH (opposite side divided by the hypotenuse)

solve for y

$y=sin(60^o)2\sqrt{3}$

Remember that

$sin(60^o)=\frac{\sqrt{3}}{2}$

substitute

$y=(\frac{\sqrt{3}}{2})2\sqrt{3}$

$y=3\ units$

Part 2)

Let

h ----> the length of the hypotenuse

we know that

In the right triangle of the figure

$sin(45^o)=\frac{3\sqrt{2}}{h}$ ----> by SOH (opposite side divided by the hypotenuse)

$h=\frac{3\sqrt{2}}{sin(45^o)}$

Remember that

$sin(45^o)=\frac{\sqrt{2}}{2}$

substitute

$h=3\sqrt{2}:\frac{\sqrt{2}}{2}$

$h=6\ units$

7 0

3 years ago

Find an equation of the line, in point-slope form, that passes through (-2,3) with a slope of -4

Nostrana [21]

Step-by-step explanation:

let the eqn be y - y1 = m (x - x1)

sub (-2, 3) and m = -4:

y - (-2) = -4 (x - (-2))

y + 2 = -4 (x + 2)

Topic: Coordinate Geometry

If you like to venture further, feel free to check out my insta (learntionary). It would be best if you could give it a follow. I'll be constantly posting math tips and notes! Thanks!

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Answer:

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hram777 [196]

Answer:

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