![\boxed{\boxed{\pink{\bf \leadsto Hence \ option\ [d]\ \bigg(y = \dfrac{5}{2}x + 5\bigg) \ is \ correct }}}](/tpl/images/1012/2698/a400d.png)
Step-by-step explanation:
Here from the given graph we can see that the graph the graph intersects x axis at (2,0) and y axis at (5,0). On seeing options it's clear that we have to use Slope intercept form . Which is :-
![\large\boxed{\orange{\bf y = mx + c} }](/tpl/images/1012/2698/c6a96.png)
We know that slope is
. So here slope will be ,
![\red{\implies slope = \tan\theta} \\\\\implies slope =\dfrac{PERPENDICULAR}{BASE} \\\\\bf \implies slope =\dfrac{5}{2}](/tpl/images/1012/2698/49145.png)
Hence the slope is 5/2 . And here value of c will be 5 since it cuts y axis at (5,0).
![\purple{\implies y = mx + c }\\\\\implies y = \dfrac{5}{2}x + 5 \\\\\underline{\boxed{\red{\tt \implies y = \dfrac{5}{2}x + 5 }}}](/tpl/images/1012/2698/fa359.png)
Hence option [ d ] is correct .