Answer:
The equation of the line in
form where
are integers with no factor common to all three, and greater than or equal 0 is:
![x+3y=12](https://tex.z-dn.net/?f=x%2B3y%3D12)
Step-by-step explanation:
Given:
x-intercept = 12
y-intercept = 4
To find the equation of line in the form
where
are integers with no factor common to all three, and greater than or equal 0.
Solution:
The x-intercept is the point at which the line cuts the x-axis. The point of x-intercept is given as ![(x,0)](https://tex.z-dn.net/?f=%28x%2C0%29)
Thus, on point of the line is (12,0)
The y-intercept is the point at which the line cuts the y-axis. The point of y-intercept is given as
.
Thus, on point of the line is (0,4)
Using the two points we can find the slope of the line using the slope formula.
![m=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
So, slope of the line can b given as:
![m=\frac{4-0}{0-12}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B4-0%7D%7B0-12%7D)
![m=\frac{4}{-12}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B4%7D%7B-12%7D)
![m=-\frac{1}{3}](https://tex.z-dn.net/?f=m%3D-%5Cfrac%7B1%7D%7B3%7D)
The slope intercept form of the equation of he line is given as:
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
where
represents slope of the line and
represents the y-intercept.
So, the equation of the line can be given as:
![y=-\frac{1}{3}x+4](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B1%7D%7B3%7Dx%2B4)
Multiplying each term by 3 to remove fraction.
![3y=3.-\frac{1}{3}x+4(3)](https://tex.z-dn.net/?f=3y%3D3.-%5Cfrac%7B1%7D%7B3%7Dx%2B4%283%29)
![3y=-x+12](https://tex.z-dn.net/?f=3y%3D-x%2B12)
Adding
both sides.
![3y+x=-x+x+12](https://tex.z-dn.net/?f=3y%2Bx%3D-x%2Bx%2B12)
![3y+x=12](https://tex.z-dn.net/?f=3y%2Bx%3D12)
Thus, the equation of the line in
form where
are integers with no factor common to all three, and greater than or equal 0 is:
![x+3y=12](https://tex.z-dn.net/?f=x%2B3y%3D12)