Answer:
1) For, m = 3/4 , (0,4) , 4y - 16 - 3x = 0 is the equation of line.
2) For, m = 4 , (-2,-5) , y - 4x - 4 = 0 is the equation of line.
3) For, m = -1/3 , (4,-1) , x + 3y -1 = 0 is the equation of line.
Step-by-step explanation:
If m is the slope and (x0,y0) is the point on any given equation, then
by POINT SLOPE FORMULA:
The line equation is given as (y - y0) = m (x -x0)
Now , here:
<u>1) m = 3/4 , (x0, y0) = (0.4)</u>
So,, the equation of line is ![(y-4) = \frac{3}{4} (x-0)\\or, 4(y-4) = 3x](https://tex.z-dn.net/?f=%28y-4%29%20%3D%20%5Cfrac%7B3%7D%7B4%7D%20%28x-0%29%5C%5Cor%2C%204%28y-4%29%20%20%3D%20%203x)
on simplification, 4y - 16 - 3x = 0 is the equation of line.
<u>2)</u><u> m = 4 , (x0, y0) = (-2.-5)</u>
So,, the equation of line is ![(y-(-5)) = 4 \times (x-(-2))\\or, (y+4) = 4(x+2)](https://tex.z-dn.net/?f=%28y-%28-5%29%29%20%3D%204%20%5Ctimes%20%28x-%28-2%29%29%5C%5Cor%2C%20%28y%2B4%29%20%20%3D%20%204%28x%2B2%29)
on simplification, y - 4x - 4 = 0 is the equation of line.
<u>3) m = -1/3 , (x0, y0) = (4, -1)</u>
So,, the equation of line is ![(y-(-1)) = \frac{-1}{3} (x-4)\\or, 3(y+1) = -(x-4)](https://tex.z-dn.net/?f=%28y-%28-1%29%29%20%3D%20%5Cfrac%7B-1%7D%7B3%7D%20%28x-4%29%5C%5Cor%2C%203%28y%2B1%29%20%20%3D%20%20-%28x-4%29)
on simplification, x + 3y -1 = 0 is the equation of line.