The Equation of a Line
The slope-intercept form of a line can be written as:
y = mx + b
Where m is the slope of the graph of the line and b is the y-intercept.
In the specific case where the line passes through the origin (0,0), we can find the value of b by substituting x=0 and y=0:
0 = m(0) + b
Solving for b:
b = 0.
Thus, the equation of the line reduces to:
y = mx
We only need to find the value of the slope.
That is where we need the second data. Our line is perpendicular to the line of equation 4x + 3y = 6.
Solving for y:
![y=-\frac{4}{3}x+2](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B4%7D%7B3%7Dx%2B2)
The slope of the second line is -4/3.
We must recall that if two lines of slopes m1 and m2 are perpendicular, then:
![m_1\cdot m_2=-1](https://tex.z-dn.net/?f=m_1%5Ccdot%20m_2%3D-1)
Substituting the value of m1 and solving for m2:
![\begin{gathered} -\frac{4}{3}\cdot m_2=-1 \\ m_2=\frac{3}{4} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20-%5Cfrac%7B4%7D%7B3%7D%5Ccdot%20m_2%3D-1%20%5C%5C%20m_2%3D%5Cfrac%7B3%7D%7B4%7D%20%5Cend%7Bgathered%7D)
The slope of our line is 3/4 and the required equation is:
![y=\frac{3}{4}x](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B3%7D%7B4%7Dx)
From this last equation, we need to find the general form of the line.
Multiply both sides of the equation by 4:
4y = 3x
Subtract 3x on both sides:
4y - 3x = 0
Reorder:
-3x + 4y = 0