Question

7000 shirts can be sold for $61.00 and 8000 shirts can be sold for $52.00, How do you give linear equation p=mn+b?

Answer 1

`y = -9/1000x + 124`

Explanation:

We are basically given two points: (7000, 61) and (8000, 52). Therefore we can use the point-slope formula to find the linear equation in slope-intercept form.

First, we need to find the slope. The formula for the slope given two points is:

`color(red)(m = (y_2 = y_1)/(x_2 - x_1)`
Where `m` is the slope and `(x_1, y_1)` and `(x_2, y_2)` are the two points.

Substituting the points we were provided gives:

`m = (52 - 61)/(8000 - 7000)`

`-9/1000`

Next we can use the point-slope formula to give us the linear equation:

The point-slope formula states: `color(red)((y - y_1) = m(x - x_1))`
Where `m` is the slope and #(x_1, y_1) is a point the line passes through.

Using the slope we calculate and either of the points we can substitute to get the equation:

`y - 52 = -9/1000(x - 8000)`

Now we can solve for `y` to get the equation in the slope-intercept form:

`y - 52 = -9/1000x + (9 xx 8000)/1000`

`y - 52 = -9/1000 + 72000/1000`

`y - 52 = -9/1000x + 72`

`y - 52 + 52 = -9/1000x + 72 + 52`

`y = -9/1000x + 124`