the equation of stralight line is 3x+2y=11 find the equation of the parrallel line passing through the point 2,5
i got y=2/3x +7 1/3
or is it y=2/3x -4.5
$\displaystyle 3x+2y=11$
$\displaystyle 2y=-3x+11$
$\displaystyle y=-\frac{3}{2}x+\frac{11}{2}$
Slope(m) = $\displaystyle -\frac{3}{2}$
Use slope-intercept form of the linear equation: y=mx+b and (2, 5) and solve for b.
$\displaystyle y=mx+b$
$\displaystyle 5=-\frac{3}{2}(2)+b$
$\displaystyle 5=-3+b$
$\displaystyle 8=b$
Substituting back into y=mx+b, we have:
$\displaystyle y=-\frac{3}{2}x+8$
In that case, just change the slope to $\displaystyle \frac{2}{3}$ which is the negative reciprocal of $\displaystyle -\frac{3}{2}$ and then proceed the same way.
$\displaystyle 5=\frac{2}{3}(2)+b$
$\displaystyle 5=\frac{4}{3}+b$
$\displaystyle \frac{11}{3}=b$
The equation of the perpendicular is $\displaystyle y=\frac{2}{3}x+\frac{11}{3}$