Question

Write the equation for the linear relationship in slope-intercept form.

Javi regularly checks his balance on his bus pass. Friday afternoon, his balance was $26.25. Monday morning, his balance was $1.50.
Basically, what would be the 2 ordered pairs to describe that relationship?

Answer 1

The two points can be:

(0, $26.25) and (3, $1.50)

Where this function is the balance as a function on the number of days.

And the equation is:

y = -$8.25*x + $26.25

Explanation:

Let's define Friday as our day 0, we know that on Friday his balance was $26.25

Then we have the ordered pair (0, $26.25)

Monday is 3 days after Friday, then this will be day number 3, and on Monday his balance was $1.50, then we have the ordered pair (3, $1.50)

Now that we have two ordered pairs, we can talk about linear relationships.

A line is written as:

y = a*x + b

where a is the slope and b is the y-intercept.

IIf we have a line that passes through the points (x1, y1) and (x2, y2) then the slope of the line is:

a = (y2 - y1)/(x2 - x1)

Then whit the points (0, $26.25) and (3, $1.50) we can find the slope of our line:

a = ($1.50 - $26.25)/(3 - 0) = -$8.25

Then our line is:

y = -$8.25*x + b

To find the value of b we can just replace the point (0, $26.25), this means that we need to replace x by 0, and y by $26.25

$26.25 = -$8.25*0 + b

$26.25 = b

Then the linear equation will be:

y = -$8.25*x + $26.25