Question

A line with slope 2/3 contains point M(0,10). If you were standing on the x-y plane at point M, and walked 12 units straight down, then straight left to the line, what is the x-coordinate of the point were you would be standing?

Answer 1

The x-coordinate of the point where you would be standing is -18.

Step-by-step explanation:

To find the x-coordinate of the point where you would be standing, we need to determine the equation of the line passing through point M(0,10). We know that the slope of the line is 2/3, so we can write the equation in the form y = mx + b, where m is the slope and b is the y-intercept. Since the line passes through point M(0,10), we can substitute the coordinates into the equation to find the value of b:

10 = (2/3)(0) + b

10 = b

Therefore, the equation of the line is y = (2/3)x + 10.

Now, we can find the x-coordinate of the point where you would be standing. If you walk 12 units straight down from point M(0,10), your new y-coordinate would be 10 - 12 = -2. To find the corresponding x-coordinate, we can substitute the new y-coordinate into the equation of the line:

-2 = (2/3)x + 10

Solving for x:

(2/3)x = -12

x = (-12)(3/2) = -18

Therefore, the x-coordinate of the point where you would be standing is -18.