whe then increased her distance by .75 miles each additional time she rode.
since the change is a constant value each time, this becomes a straight line equation.
there are two formulas that could be used.
the first formula would be An = A1 + (n-1) * d
when n = 10, the formula becomes A10 = A1 + 9 * .75
A1 is 6.5, so the formula becomes A10 = 6.5 + 9 * .75.
solve for A10 to get:
A10 = 13.25
the second formula is the slope intercept form of the equation for a straight line.
that formula is y = mx + b
m is the slope and b is the y-intercept.
you are given the slope and one point on the line.
the slope is .75 and the given point is (1,6.5)
with a slope of.75, the formula becomes y = .75 * x + b
to find the value of b, replace x with 1 and y with 6.5 and provide the slope of .75 to get:
6.5 = .75 * 1 + b
solve for b to get:
b = 6.5 - .75 = 5.75
the formula becomes y = .75 * x + 5.75
when x = 10, the formula becomes y = .75 * 10 + 5.75
solve for y to get y = 13.25
for graphing purposes, y = .75 * x + 5.75 can stand as is.
for graphing purposes, An = 6.5 + (n-1) * .75 can be written as:
y = 6.5 + (x-1) * .75
these two equations equivalent, meaning they will provide the same answer for any value of x.
you can also show they're equivalent by doing the following to the second equation.
y = 6.5 + (x - 1) * .75 becomes:
y = 6.5 + .75 * x - .75
combine like terms to get:
y = .75 * x + 5.75.
the second form of the equation has been shown to be the same as the first form of the equation, since both equations are identical.
your solution is that her distance on the 10th day is 13.25 miles.
here is the graph of both equations.
both equations draw the same identical line on the graph since the equations are identical.
