Question

Find a vector that is parallel to -9x+2y = 10. Please explain step by step

Answer 1

Answer:

Step-by-step explanation:

Step One: Find the slope of the given Line

2y - 9x = 10                   Add 9x to both sides

2y - 9x + 9x = 9x + 10  Combine

2y = 9x + 10

y = 9/2 x + 5

The parallel line has a slope of 9/2

Step Two: Find the magnitude

sqrt(x^2 + y^2) = r                   You don't have a magnitude. Invent one, r

x^2 + y^2 = r^2                        Both sides have been squared

Step Three: Find the change in y / x

y / x = 9/2

Step Four: Find the value of y

y/x = 9/2                 Multiply both sides by x

y = 9/2 * x

Step Five: Solve for x

x^2 + y^2 = r^2

x^2 +(9/2x)^2 = r^2

x^2 + 81x^2 / 4 = r^2                Change the 1 to common denominator 1 = 4/4

4/4 x^2 + 81x^2/ 4 = r^2

85 x^2/ 4 = r^2                        Multiply both sides by 4/85

4/85 * (85 / 4) x^2 = 4/85 r^2  

x^2 = 4/85 r^2                         Take the square root of both sides

x = +/- 2/sqrt(85) r                   Rationalize the denominator  

x = (+/- 2 sqrt(85) ) / 85 *

Step Six: Solve for y

y = 9/2 x

y = 9/2 * 2 sqrt(85) / 85      Cancel the 2s

y = +/- 9* sqrt(85)/85

Answer

<2*sqrt(85)/85 ,  9 sqrt(85)/85>

You can write the minus answer if you need it. I kind of suspect you won't.