Changing the equation into slope form:
![y = mx + c](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20c)
, where
![m](https://tex.z-dn.net/?f=m)
is the slope [gradient] and
![c](https://tex.z-dn.net/?f=c)
is the y-intercept.
![2x+3y=1470](https://tex.z-dn.net/?f=2x%2B3y%3D1470)
![3y = -2x+1470](https://tex.z-dn.net/?f=3y%20%3D%20-2x%2B1470)
![y= - \frac{2}{3}x+ \frac{1470}{3}](https://tex.z-dn.net/?f=y%3D%20-%20%5Cfrac%7B2%7D%7B3%7Dx%2B%20%5Cfrac%7B1470%7D%7B3%7D%20)
![y=- \frac{2}{3}x+490](https://tex.z-dn.net/?f=y%3D-%20%5Cfrac%7B2%7D%7B3%7Dx%2B490%20)
The gradient is
![- \frac{2}{3}](https://tex.z-dn.net/?f=-%20%5Cfrac%7B2%7D%7B3%7D%20)
and y-intercept is at
![y=490](https://tex.z-dn.net/?f=y%3D490)
Graphing
![y=- \frac{2}{3}x+490](https://tex.z-dn.net/?f=y%3D-%20%5Cfrac%7B2%7D%7B3%7Dx%2B490%20)
using slope-intercept method:
a) The slope is a negative slope. The line will go 'down hill'
b) The line must pass the point (0, 490)
c) The line will intercept the x-axis at y = 0
![x = 735](https://tex.z-dn.net/?f=x%20%3D%20735)
So, x-intercept is at (735, 0)
The graph of this function is shown below. The intercepts are labelled at:
y = 490
x = 735
-----------------------------------------------------------------------------------------------------------
Next month's profit equation
![2x+3y=1593](https://tex.z-dn.net/?f=2x%2B3y%3D1593)
Rewriting this into slope-equation form
![3y = -2x+1593](https://tex.z-dn.net/?f=3y%20%3D%20-2x%2B1593)
![y=- \frac{2}{3}+ \frac{1593}{3}](https://tex.z-dn.net/?f=y%3D-%20%5Cfrac%7B2%7D%7B3%7D%2B%20%5Cfrac%7B1593%7D%7B3%7D%20)
![y= - \frac{2}{3}+531](https://tex.z-dn.net/?f=y%3D%20-%20%5Cfrac%7B2%7D%7B3%7D%2B531%20)
The gradient,
![m](https://tex.z-dn.net/?f=m)
, equals to
![- \frac{2}{3}](https://tex.z-dn.net/?f=-%20%5Cfrac%7B2%7D%7B3%7D%20)
The y-intercept,
![c](https://tex.z-dn.net/?f=c)
, equals to 531
The equation still has the same gradient with last month's profit equation but different y-intercept.
-------------------------------------------------------------------------------------------------------------
A linear graph show points of (0, 300) and (450, 0)
We work out the slope:
![\frac{300-0}{0-450} = \frac{300}{-450}=- \frac{20}{30} =- \frac{2}{3}](https://tex.z-dn.net/?f=%20%5Cfrac%7B300-0%7D%7B0-450%7D%20%3D%20%5Cfrac%7B300%7D%7B-450%7D%3D-%20%5Cfrac%7B20%7D%7B30%7D%20%20%3D-%20%5Cfrac%7B2%7D%7B3%7D%20)
Y-intercept at x = 0, so it's at y = 300
Equation