For this problem, we can refer to the slope formula [tex]\frac{y2 - y1}{x2 - x1}[/tex]. This describes the rise over run, change in x over y. We know that the y axis represents the dependent variable and that the x axis represents the independent variable. To put this in the equation, note the use of the word 'per' in this question. If she earns 5 dollars per hour of babysitting, then this means that the amount she earns depends on the number of hours she works. To put this numerically:
[tex]\frac{5(dollars)}{1(hour)}[/tex]
Think of the line that separates the dividend and divisor as the word 'per'. The slope of this line would be 5x, since y increases by five every time x increases by one. This means that your slope is [tex]y(dollars) = 5x(hours)[/tex].
We are still not completely finished. Notice the fact that she is paid an additional $3 for her transportation. This means that the y value for this line does not start out from 0. Before working any hours at all, there were 3 dollars, which is called the equation's y intercept. Your complete equation will be:
[tex]y(dollars) = 5(hours) + 3[/tex]
Now that it's complete, all there's left to do is plug in the values for hours worked.
3 hours:
[tex]y = 5(3) + 3[/tex]
-->[tex]y = 15 + 3[/tex]
--->[tex]y = 18[/tex]
She will earn $18 dollars for 3 hours.
8 hours:
[tex]y = 5(8) + 3[/tex]
-->[tex]y = 40 + 3[/tex]
---> [tex]y = 43[/tex]
She will earn $43 in 8 hours.
Hope this helped.
