"The minute of a hand clock moves 1/10 degree every second. If you look at the clock when the minute hand is 10 degrees past the 12, you can use the equation y=1/2x+10 to find how many degrees past the 12 the minute hand is after x seconds. Graph the equation and tell whether it is linear." I understand that this equation is linear, but I'm not sure what numbers to replace the x and y variables with. How would I go about solving this problem?

Question

"The minute of a hand clock moves 1/10 degree every second. If you look at the clock when the minute hand is 10 degrees past the 12, you can use the equation y=1/2x+10  to find how many degrees past the 12 the minute hand is after x seconds. Graph the equation and tell whether it is linear."  I understand that this equation is linear, but I'm not sure what numbers  to replace the x and y variables with. How would I go about solving this problem?

whpalmer4 · Answer

The equation doesn't seem to be correct.  If the hand moves $0.1^\circ/\text{s}$ , and y is the position of the hand in degrees, at t = 0, y = 10 degrees.  After 10 seconds, it should have moved $$0.1^\circ/\text{s} * 10 \text{ s} = 1^\circ $$ which means $y = 10 + 1 =  11$, but the formula given would give us $y = \frac{1}{2}x + 10 = \frac{1}{2}(10) + 10 = 15$.

anonymous · Answer

Thank you. I asked my mum, but she doesn't know math >.< I'll question my teach
er later.

whpalmer4 · Answer

But no matter, it can be some alien clock :-)

Would the equation make more sense to you if I wrote $\theta = \frac{1}{2}t + 10$? Here $\theta$ is the angle, and $t$ is the elapsed time in seconds.  The graph will look exactly the same, except for the labels on the axes.