Match the information on the left with the appropriate equation on the right.

See attachment below

Step-by-step explanation:

For the first option, we are given m = - 2 / 3, b = 3. This is likely in the point - slope form y = mx + b, where m = slope and b = y - intercept. Thus, the equation of the line in point - slope form given this information, should be y = - 2 / 3x + 3. It seems as if none of the following equations match this form, so let us interchange the equation a bit,

y = - 2 / 3x + 3,

y + 2 / 3x = 3,

2x + 3y = 9 - Option C

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Next we are given m = - 3 / 2, and that this line passes through the point ( 4, - 1 ). Substitute m as - 3 / 2, x as 4, y as - 1, knowing point ( 4, - 1 ), into the form y = mx + b - solving for b.

- 1 = ( - 3 / 2 )( 4 ) + b,

b = 5,

Thus the equation in point - slope form should be y = - 3 / 2x + 5. None of the choices match this, so let us again alter the equation,

y = - 3 / 2x + 5,

2y = - 3x + 10,

- 2y = 3x - 10 - Option A

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( 6, 3 ) and ( 3, 1 ) is given to lie on this line. The slope of the line should be as follows,

Slope = 3 - 1 / 6 - 3 = 2 / 3

Now let us determine the y - intercept ( b ) by substitute one of the points, say ( 6, 3 ). In this case x = 6, and y = 3,

3 = ( 2 / 3 )( 6 ) + b,

b = - 1,

y = 2 / 3x - 1 = Option D

Take a look at the attachment below for further help;

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west