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3 years ago

Give the equation of the line through the point ( - 10,9) with a slope of -1/5

Mathematics

1 answer:

hichkok12 [17]3 years ago

7 0

Equation of the line in slope-intercept form is y = -1/5 x + 9

Step-by-step explanation:

Step 1: Given slope of the line is -1/5 and the point is (-10, 9). Here m=-1/5.

⇒ y = -1/5 x + b ------ (1)

Step 2: Find the y-intercept of the line, b. Since the line passes through (-10, 9) substitute x = -10 and y = 9 in eq(1)

⇒ 9 = -1/5 × -10 + b = 2 + b

⇒ b = 9 - 2 = 7

Step 3: Slope intercept form of the line is y = mx + b. Form the equation using the values of m and b.

⇒ y = -1/5 x + 7

It can also be written as 5y + x = 35

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PEMDAS
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) find a vector parallel to the line of intersection of the planes 5x − y − 6z = 0 and x + y + z = 1.

snow_tiger [21]

The cross product of the normal vectors of two planes result in a vector parallel to the line of intersection of the two planes.

Corresponding normal vectors of the planes are
<5,-1,-6> and <1,1,1>

We calculate the cross product as a determinant of (i,j,k) and the normal products

i j k
5 -1 -6
1 1 1

=(-1*1-(-6)*1)i -(5*1-(-6)1)j+(5*1-(-1*1))k
=5i-11j+6k
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Check orthogonality with normal vectors using scalar products
(should equal zero if orthogonal)
<5,-11,6>.<5,-1,-6>=25+11-36=0
<5,-11,6>.<1,1,1>=5-11+6=0

Therefore <5,-11,6> is a vector parallel to the line of intersection of the two given planes.

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3 years ago

Solve for x 8 is to 64 as 2 is to X

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2 years ago

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What is the slope of the line?

postnew [5]

Answer:

its 2

Step-by-step explanation:

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3x+4y-3z=4;5x-y+2z=3;x+2y-z=-2 Solving Systems in three variables

Harlamova29_29 [7]

Answer: x = 3, y = 1, z = 2

Step-by-step explanation:

EQ 1: x - y - z = 0

EQ 3: -x + 2y + z = 1

y = 1

EQ 2: 2x - 3y + 2z = 7 → 1(2x - 3y + 2z = 7) → 2x - 3y + 2z = 7

EQ 3: -x + 2y + z = 1 → -2( -x + 2y + z = 1) → -2x + 4y + 2z = 2

y + 4z = 9

y = 1 ⇒ 1 + 4z = 9

4z = 8

z = 2

Input y = 1 and z = 2 into one of the equations to solve for x:

EQ 1: x - y - z = 0

x - (1) - (2) = 0

x - 3 = 0

x = 3

Check:

EQ 2: 2x - 3y + 2z = 7

2(3) - 3(1) + 2(2) = 7

6 - 3 + 4 = 7

3 + 4 = 7

7 = 7 $\checkmark$

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3 years ago