Question

Help would be appreciated

Answer 1

1.5 miles less

Explanation:

Step 1: Find equation for Alexanda

• We can see from Fabian's equation that there is a linear relationship between miles (y) and gallons (x).

• Fabian's equation is in the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

• Although we're not given the equation for Alexandra, we can find it using the slope formula, which is

`m=(y_(2)-y_(1) )/(x_(2)-x_(1) )`.

If we allow (8, 345.6) to be our x1 and y1 and (12, 518.4) to be our x2 and y2, our slope is

`m=((518.4-345.6))/((12-8))\\ m=(172.8)/(4)\\ m=43.2`

• Now, we must find the y-intercept by plugging in 43.2 for m, 8 for x, and 345.6 for y into the general slope-intercept form and solving for b:

`345.6=43.2(8)+b\\345.6=346.6+b\\0=b`

Thus, the equation for Alexandra is y = 43.2x

Step 2: Plug in 1 for x for both Fabian and Alexandra's equations and subtract

Since x is is gallons, we plug in 1 for x for each equation and subtract Fabian's miles from Alexandra's miles to find how many miles less can Fabian drive one 1 gallon of gas than Alexandra:

Fabian: y = 41.7(1) = 41.7

Alexandra: y = 43.2(1) = 43.2

Difference of Alexandra and Fabian's miles: 43.2 - 41.7 = 1.5