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)?

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Answer 1 · 2016-02-10T03:21:09

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

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

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

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

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

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

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

$3 y = 4 x - 10$ $3y=4x-10$ or

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

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