91Ó°ÊÓ

The given data can be listed below as:

• The spatial separation between the event 1 and 2 is ${\mathrm{Δ³\ae }}^{\text{'}}$.
• The temporal separation between the event 1 and 2 is ${\mathrm{Δ³Ù}}^{\text{'}}$.
• The value of the vertical axis is ${\mathrm{Δ³\ae }}_{\mathrm{a}}=10.0\text{″¾}$.

The slope of a graph is described as the steepness measure of a graph. The slope mainly stays constant.

According to the line of the graph, it consists of an equation. The equation of the ${\mathrm{Δ³\ae }}^{\text{'}}$is expressed as:

$\begin{array}{c}\mathrm{Δ³\ae }={\mathrm{vΔ³Ù}}^{\text{'}}+{\mathrm{γΔ³\ae }}^{\text{'}}\\ ={\mathrm{sΔ³Ù}}^{\text{'}}+\mathrm{a}\end{array}$

Here,$\mathrm{a}$is the y-intercept of the graph and$\mathrm{γ}$is the x-intercept.

Equalling both the sides of the above equation, the value of${\mathrm{Δ³\ae }}^{\text{'}}$is expressed as:

$\begin{array}{c}{\mathrm{γΔ³\ae }}^{\text{'}}=\mathrm{a}\\ {\mathrm{Δ³\ae }}^{\text{'}}=\frac{\mathrm{a}}{\mathrm{γ}}\end{array}$

From the graph, it can be observed that the value of y-intercept is about $2.0\text{″¾}$and $\mathrm{γ}$also comes to a value of $2.54$.

Substitute$2.0\text{″¾}$ for$\mathrm{a}$ and $2.54$for $\mathrm{γ}$in the above equation.

$\begin{array}{c}{\mathrm{Δ³\ae }}^{\text{'}}=\frac{2.0\text{″¾}}{2.54}\\ =0.78\text{″¾}\end{array}$

Thus, the value ofrole="math" localid="1663054925380" $∆x\text{'}$ is$0.78\text{″¾}$