Question

Write an equation in slope-intercept form of the line perpendicular to y = - 1 5 x + 1 4 that passes through the point (3, 4).

Answer 1

The equation of the line is $y=\frac{1}{15} x+\frac{19}{5}$

Explanation:

The equation is $y=-15x+14$ 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 $y=m x+b$, we shall find the value of slope.

Thus, slope m = -15

Since, the line is perpendicular, the negative slope is given by $\frac{-1}{m}$

Thus, the new slope is $m=\frac{1}{15}$

Now, we shall find the equation of the line perpendicular to the slope $\frac{1}{15}$ is

$y-y_{1}=\frac{1}{15} \left(x-x_{1}\right)$

Let us substitute the points (3,4), we have,

$y-4=\frac{1}{15} \left(x-3\right)$

Muliplying the term within the bracket, we get,

$y-4=\frac{1}{15}x-\frac{1}{5}$

Adding both sides of the equation by 4, we get,

$y=\frac{1}{15}x-\frac{1}{5}+4$

Adding the like terms, we have,

$y=\frac{1}{15} x+\frac{19}{5}$

Thus, the equation in slope intercept form of the line is $y=\frac{1}{15} x+\frac{19}{5}$