Answer:
Nirmala can use the lamp for 31.66 hours before it runs out of oil.
Step-by-step explanation:
From the graph,
Take any two points, let say
(15, 25)
(25, 10)
[tex]\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(15,\:25\right),\:\left(x_2,\:y_2\right)=\left(25,\:10\right)[/tex]
[tex]m=\frac{10-25}{25-15}[/tex]
[tex]m=-\frac{3}{2}[/tex]
The equation of line in slope-intercept form
[tex]y = mx + b[/tex]
Putting [tex]m=-\frac{3}{2}[/tex] and any point, let say (25, 10), to find the y-intercept 'b'
[tex]10=-\frac{3}{2}\left(25\right)+b[/tex]
[tex]-\frac{3}{2}\left(25\right)+b=10[/tex]
[tex]-\frac{75}{2}+b=10[/tex]
[tex]\mathrm{Add\:}\frac{75}{2}\mathrm{\:to\:both\:sides}[/tex]
[tex]-\frac{75}{2}+b+\frac{75}{2}=10+\frac{75}{2}[/tex]
[tex]b=\frac{95}{2}[/tex]
[tex]b=47.5[/tex]
So the equation of line will be:
[tex]y = mx + b[/tex]
[tex]y=-\frac{3}{2}x+47.5[/tex]
In order to find how long Nirmala can use the lamp before it runs out of oil, we need to find x-intercept which can be obtained by putting y = 0, and solve for x, as duration lies on x-axis.
so
[tex]y=-\frac{3}{2}x+47.5[/tex]
Putting y = 0
[tex]0=-\frac{3}{2}x+47.5[/tex]
[tex]-\frac{3}{2}x+47.5=0[/tex]
[tex]-\frac{3}{2}x=-47.5[/tex]
[tex]\mathrm{Multiply\:both\:sides\:by\:}2[/tex]
[tex]2\left(-\frac{3}{2}x\right)=2\left(-47.5\right)[/tex]
[tex]-3x=-95[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}-3[/tex]
[tex]\frac{-3x}{-3}=\frac{-95}{-3}[/tex]
[tex]x=\frac{95}{3}[/tex]
[tex]x=31.66[/tex]
Therefore, Nirmala can use the lamp for 31.66 hours before it runs out of oil.
