# If line allb and line A has the equation 8x-6y+9=0, determine the equation of line b, in point-slope form if b passes (1,-2)?

## If line allb and line A has the equation 8x-6y+9=0, determine the equation of line b, in point-slope form if b passes (1,-2)?

Feb 10, 2016

$y = \frac{4}{3} \cdot x - \frac{10}{3}$

#### Explanation:

A line parallel to $8 x - 6 y + 9 = 0$ will be $8 x - 6 y + c = 0$.

As it passes through $\left(1 , - 2\right)$, putting these values in the latter

$8 \left(1\right) - 6 \left(- 2\right) + c = 0$ gives $c = - 8 - 12$

i.e. $c = - 20$ i.e. the equation of line is

$8 x - 6 y - 20 = 0$ or $4 x - 3 y - 10 = 0$

For converting it to point-slope form, one has to get the value of $y$ in terms of $x$. In this equation,

$3 y = 4 x - 10$ or

$y = \frac{4}{3} \cdot x - \frac{10}{3}$

where $\frac{4}{3}$ is slope and $- \frac{10}{3}$ is intercept on $y$ axis.