Addition & Subtraction of Errors

Q. The sum of the slopes of two lines passing through the origin is zero. If one line passes through $(a,4)$ and another line passes through $(-3,b)$, then which of the following can be the values of a and b?

1. $a=2,b=6$
2. $a=4,b=3$
3. All of the above
4. $a=-3,b=-4$

Q.

The mass of Mr x is 50kg and the uncertainty in measurement is 1 kg.The mass of Mr y is 55kg and the uncertainty in measurement is 2 kg. Find the difference of their masses with correct uncertainties.

1. 5 $\pm$ 3 kg

2. None of these

3. 105 $\pm$ 3 kg

4. 5 $\pm$ 1 kg

Q. Three cars start at the same time and travel at different constant rates. The motion is represented in the graph for car A and car B. The equation of motion of the car A: $0.5y=25x$. Throughout the journey, car C remains equidistant from car B and car A. What will be the distance traveled by car C when car A has traveled $300$ miles?
[Hint: Average speed = Slope of the distance-time graph $=\frac{\text{Distance traveled}}{\text{Time taken}}$]

Q. Ester and Robert calculated slope for different sets of data. Ester found an equation as $3y=x$ for the given table and Robert calculated slope $=2$ for the given graph.

$x$	$1.5$	$3.5$	$7$
$y$	$4.5$	$10.5$	\$21$

Choose the correct statement.