Answer:
[tex]\huge\boxed{2329 \ \text{pounds}}[/tex]
Step-by-step explanation:
In order to solve this equation, let's see what we already know.
- We know two points on the graph which we can use to find the slope
That's about it.
However, this can come useful to find the slope between the two points, which is the slope for the entire graph (since this is linear). The slope between two points is usually defined as [tex]\frac{\Delta y}{\Delta x}[/tex] (change in y / change in x). Our two points are (18, 2017) and (48, 2212).
The change in y between our two points is [tex]2212-2017 = 195[/tex], and the change in x is [tex]48 - 18 = 30[/tex]. Our slope will then be [tex]\frac{195}{30}[/tex], which comes out to be approximately 6.5. Therefore, our slope is 6.5.
Now that we know the slope, we can substitute inside our equation in slope intercept form.
[tex]y = 6.5x+b[/tex]
We have yet to find b, the y-intercept (how much the plane itself weighs). To find b, we can substitute a point on the graph into the equation and solve for b. We know that the point (18, 2017) is on the graph so let's use that.
- [tex]2017 = 6.5 \cdot18 + b[/tex]
- [tex]2017 = 117 + b[/tex]
- [tex]1900= b[/tex]
Now that we know our y-intercept is 1900, we can create our equation by using the slope and the y-intercept.
[tex]y=6.5x+1900[/tex]
Finally, to find the weight of the plane with 66 pounds of fuel, we can substitute 66 inside this equation as x.
- [tex]y = 6.5 \cdot66+ 1900[/tex]
- [tex]y = 429+1900[/tex]
- [tex]y=2329[/tex]
So the plane weighed 2329 pounds with 66 gallons of fuel.
Hope this helped!
