The following equation for the variation of two quantities x and t, x=a+b where a and b are contant. Use the data below to plot a suitable linear graph and hence determine the value of a and b

The given equation is $x = a + b\sqrt{t}$. This equation can be rearranged into the form of a straight line equation, $Y = mX + c$, where:

For each given value of $t$, calculate the corresponding value of $\sqrt{t}$. You will then have a set of $(X, Y)$ data points, which are $(\sqrt{t}, x)$.

Plot the values of $x$ on the y-axis against the values of $\sqrt{t}$ on the x-axis. Draw the best-fit straight line through the plotted points.

• The value of $a$ is the y-intercept of the straight line (the point where the line crosses the y-axis, i.e., when $\sqrt{t} = 0$).
• The value of $b$ is the gradient (slope) of the straight line. You can calculate the gradient using any two points $(X_1, Y_1)$ and $(X_2, Y_2)$ on the best-fit line:

Once you provide the data, I can perform these calculations and determine the specific values for $a$ and $b$.