Respuesta :
The equation of the line is [tex]y=\frac{1}{15} x+\frac{19}{5}[/tex]
Explanation:
The equation is [tex]y=-15x+14[/tex] and passes through the point (3,4)
To find the equation of the line in slope intercept form, first we shall find the slope.
This equation is of the slope-intercept form [tex]y=m x+b[/tex], we shall find the value of slope.
Thus, slope m = -15
Since, the line is perpendicular, the negative slope is given by [tex]\frac{-1}{m}[/tex]
Thus, the new slope is [tex]m=\frac{1}{15}[/tex]
Now, we shall find the equation of the line perpendicular to the slope [tex]\frac{1}{15}[/tex] is
[tex]y-y_{1}=\frac{1}{15} \left(x-x_{1}\right)[/tex]
Let us substitute the points (3,4), we have,
[tex]y-4=\frac{1}{15} \left(x-3\right)[/tex]
Muliplying the term within the bracket, we get,
[tex]y-4=\frac{1}{15}x-\frac{1}{5}[/tex]
Adding both sides of the equation by 4, we get,
[tex]y=\frac{1}{15}x-\frac{1}{5}+4[/tex]
Adding the like terms, we have,
[tex]y=\frac{1}{15} x+\frac{19}{5}[/tex]
Thus, the equation in slope intercept form of the line is [tex]y=\frac{1}{15} x+\frac{19}{5}[/tex]
