# Line equation and Slope help!

• Jan 20th 2009, 10:41 AM
ClearSights
Line equation and Slope help!
I am in Pre-Calc and I am having trouble with these two problems...

Write an equation of a line perpendicular to 3x+2y=7 through the point (2,1).

and

Find the slope of the line connecting (4,-3) and (7,6).

If anyone could help me it would be greatly appreciated.
• Jan 20th 2009, 11:12 AM
masters
Quote:

Originally Posted by ClearSights
I am in Pre-Calc and I am having trouble with these two problems...

Write an equation of a line perpendicular to 3x+2y=7 through the point (2,1).

Hello ClearSights,

First, find the slope of the given line. We can do this by translating the equation into slope intercept form (y=mx+b).

$\displaystyle y=-\frac{3}{2}x+\frac{7}{2}$

The slope of a line perpendicular to the given line will be the "negative reciprocal" of the given line; thus $\displaystyle \frac{2}{3}$

Use this slope along with the given point (2, 1) and substitute them into the following point-slope form of a linear equation.

$\displaystyle y-y_1=m(x-x_1)$

Now, you can rearrange the above equation into other forms as required.
Quote:

Originally Posted by ClearSights
Find the slope of the line connecting (4,-3) and (7,6).

If anyone could help me it would be greatly appreciated.

Use this formula for finding the slope:

$\displaystyle m=\frac{y_2-y_1}{x_2-x_1}$
• Jan 20th 2009, 11:17 AM
ursa
Quote:

I am in Pre-Calc and I am having trouble with these two problems...

Write an equation of a line perpendicular to 3x+2y=7 through the point (2,1).

and

Find the slope of the line connecting (4,-3) and (7,6).

If anyone could help me it would be greatly appreciated.
hi
the line perpendicular to y=mx +c is
y=(-1/m)x+k
so calculate m from given equation, substitute given point and calculate k
you will get the required equation

to calculate slope formula is:
slope=(y2-y1)/(x2-x1)
• Jan 20th 2009, 11:32 AM
ClearSights
Ok, Thanks alot.