Answer:
[tex]f(x)=2.1x+3.25[/tex]
Cost for truck = $55.75.
Step-by-step explanation:
To right the linear equation in slope-intercept form, we first need to find the slop, which is defined
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Now, we choose to points from the table [tex](9, 22.15)[/tex] and [tex](16, 36.85)[/tex]. Using this points, we calculate the slope.
[tex]m=\frac{36.85-22.15}{16-9}=\frac{14.7}{7}=2.1[/tex]
Now, using one point and the slope, we find the point-slope form, which is gonna give us the slope-intercept form:
[tex]y-y_{1}=m(x-x_{1}))\\y-22.15=2.1(x-9)\\y=2.1x-18.9+22.15\\y=2.1x+3.25[/tex]
Therefore, the right choice is the first one, because it's the only one that has this linear equation.
In addition, to find the cost for a car with 25 gallons of gas size, we just have to replace this number in the x-variable:
[tex]y=2.1(25)+3.25=55.75[/tex]
Therefore, the cost for a truck with a tank size of 25 gallons, is $55.75.
