# 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?

Dec 16, 2016

$y = - \frac{9}{1000} x + 124$

#### 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 $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ are the two points.

Substituting the points we were provided gives:

$m = \frac{52 - 61}{8000 - 7000}$

$- \frac{9}{1000}$

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

The point-slope formula states: $\textcolor{red}{\left(y - {y}_{1}\right) = m \left(x - {x}_{1}\right)}$
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:

$y - 52 = - \frac{9}{1000} \left(x - 8000\right)$

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

$y - 52 = - \frac{9}{1000} x + \frac{9 \times 8000}{1000}$

$y - 52 = - \frac{9}{1000} + \frac{72000}{1000}$

$y - 52 = - \frac{9}{1000} x + 72$

$y - 52 + 52 = - \frac{9}{1000} x + 72 + 52$

$y = - \frac{9}{1000} x + 124$