# the equation of a straight line

• Oct 13th 2008, 11:05 AM
coyoteflare
the equation of a straight line
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
• Oct 13th 2008, 11:29 AM
masters
Quote:

Originally Posted by coyoteflare
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:

$\displaystyle y=-\frac{3}{2}x+8$
• Oct 13th 2008, 11:29 AM
earboth
Quote:

Originally Posted by coyoteflare
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

The LHS of the equation of the parallel must be 3x + 2y too. To calculate the RHS you only have to plug in the coordinates of the given point. Thus the equation of the parallel is:

$\displaystyle \boxed{3x+2y=16}$
• Oct 13th 2008, 11:35 AM
coyoteflare
i feel so stupid sorry i meant..
Quote:

Originally Posted by masters
$\displaystyle 3x+2y=11$

$\displaystyle 2y=-3x+11$

$\displaystyle y=-\frac{3}{2}x+\frac{11}{2}$

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:

$\displaystyle y=-\frac{3}{2}x+8$

..perpendicular.. sorry not parrallel...

getting confused cus im trying to do binomials too
• Oct 13th 2008, 11:56 AM
masters
Quote:

Originally Posted by coyoteflare
..perpendicular.. sorry not parrallel...

getting confused cus im trying to do binomials too

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 $\displaystyle y=\frac{2}{3}x+\frac{11}{3}$