Equation of a line

Question

Write an equation in point slope form of the line through the points( -3, 4 perpendicular to the line with equation
5x - 3 y =18

Answer 1

Hi Teisha,

 

Write the given line's equation point slope form (i.e., y= mx + b), 

5x - 3 y =18

3y = 5x -18

y = 5/3x - 6

You will see that the slope is 5/3

then the slope of the line perpendicular to it will be

-1/(5/3) = -3/5

 

If you plug in the values of x and y, you can find the y-intercept, b.

4 = -3/5*-3 + b

b = 11/5

Then, the equation of the line is 

y = -3/5x + 11/5

Answer 2

I shall assume that you are familiar with the Point Slope form, and that (-3,4) is a point on the desired line.

 

The line desired is perpendicular to line 5x - 3y = 18, which has slope 5/3. So OUR line will have slope -3/5, using the fact that perpendicular lines have negative reciprocal slopes (covers all cases except horizontal & vertical lines).

 

So now you know a point, and a slope for the desired line. Carry on!