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3 years ago

Find the equation for the line below

Mathematics

1 answer:

Whitepunk [10]3 years ago

6 0

Answer:

y = (-4/3)(x +4) +4

Step-by-step explanation:

Between the given points, the "rise" is -8 and the "run" is 6. The rise/run ratio is then -8/6 = -4/3. So, a version of the point-slope equation can be written:

y = m(x -h) +k . . . . . . . line with slope m through point (h, k)

y = (-4/3)(x +4) +4

_____

Comment on the answer

The image asks for "an equation", which seems to allow for any equation format. The equation shown above can be put into other forms.

y -4 = -4/3(x +4) . . . . different point-slope form

y = -4/3x -4/3 . . . . . . slope-intercept form

4x +3y = -4 . . . . . . . . standard form

4x +3y +4 = 0 . . . . . . general form

x/(-1) +y/(-4/3) = 1 . . . . intercept form

You might be interested in

2 Nine identical circles are cut from a square sheet of paper whose sides are

Ivanshal [37]

Answer:

278.64cm²

Step-by-step explanation:

Area of the sheet left out = Area of the square - Area of the 9 circles

Area of the square = L^2

L is the side length of the square

A = 36^2

Area of the square = 1296cm^2

Diameter of a circle = 38/3 = 12cm

Area of a circle = πr²

r is the radius = 12/2 = 6cm

Area of a circle = 3.14(6)²

Area of a circle = 3.14 * 36

Area of a circle = 113.04cm²

Area of 9 circles = 9 * 113.04

Area of 9 circles = 1,017.36cm²

Area of the left over = 1296 - 1,017.36

Area of the left over = 278.64cm²

6 0

3 years ago

A cube of side length s sits inside a sphere of radius r so that the vertices of the cube sit on the sphere. Find the ratio r :

svlad2 [7]

Answer:

r : s is √3 : 2

Step-by-step explanation:

The given parameter are;

A cube is inscribed in a sphere

The side length of the cube = s

The radius of the sphere = r

The ratio r : e = Required

It is noted that for a cube inscribed in a sphere, we have;

The diameter of the sphere = The diagonal of the cube

The diameter of the sphere, D = 2 × The radius = 2·r

The square of the diagonal of the cube, d² = s² + s² + s² = 3·s²

∴ The diagonal of the cube, d = (√3)·s

From the relationship between the cube and the sphere in which it is inscribed, (The diameter of the sphere = The diagonal of the cube), we have;

2·r = (√3)·s

∴ r/s = (√3)/2

r : s = √3 : 2.

8 0

3 years ago

Find the measure of each interior angle of a regular convex dodecagon. Show equations and all work that leads to your answer.

Arada [10]

The exterior angles to any convex polygon sum to 360 degrees in measure, so that for a regular dodecagon (12-gon) each exterior angle has measure

$\dfrac{360^\circ}{12}=30^\circ$

Exterior angles are complementary to interior angles, which means each interior angle has measure

$180^\circ-30^\circ=\boxed{150^\circ}$

3 0

4 years ago

MP is the angle bisector of LMN. Given that LMP is a right angle.

Akimi4 [234]

Angle bisector divides an angle into equal halves.

Angle LMN is a straight line
The measure of LMN is 180 degrees

From the question, we understand that:

MP bisects LMN

This means that:

LMN = 2 x LMP

Also, we have:

LMP = 90 ------ because LMP is a right angle

So, we have:

LMP = 2 x 90

LMP = 180

An angle that measures 180 degrees is a straight line.

Hence, the measure of LMN is 180 degrees, and it is a straight line