there is a straight line 2x+3y=12 on the Cartesian plane. How do I find a vector parallel to the line?

Answer 1

To find a vector parallel to the line 2x + 3y = 12, you can rearrange the equation into the form y = mx + b, where m is the slope of the line.

Starting with the given equation:
2x + 3y = 12

Subtract 2x from both sides:
3y = -2x + 12

Divide both sides by 3:
y = (-2/3)x + 4

Now, you can see that the coefficient of x, -2/3, is the slope of the line. A vector parallel to the line will have the same slope, so the vector is:

<1, -2/3>

Note: The vector <1, -2/3> means that for every 1 unit increase in the x-coordinate, the y-coordinate decreases by 2/3 units.