What is the slope-intercept form of the equation of the line that passes through the point (–6, 1) and is perpendicular to the graph of 2x + 3y = –5?

Question

i need help for the questions i ask if needed, so i would like to use this website to help excel in what i need to do.

Answer 1

You may convert Standard Form to slope-intercept form on every problem -- or -- you may convert Ax+By=C to y=(-A/B)x+C/B once and forever and realize that the slope is (-A/B).  The slope of a perpendicular line is the negative reciprocal (B/A), so the equation of that line is Bx-Ay = D (in this case, 3x-2y=D) and we need a point to determine D.

     3(-6)-2(1) = D

       -18 -2 = D

         -20 =D

 

The equation, in Standard Form, is:  3x-2y=-20

 

Converting that into slope-intercept form:

     3x-2y=-20

        -2y = -3x - 20

          y = (3/2)x + 10     [note:  that is y=(-A/B)x+C/B of above ]

    

Answer 2

 

To find the slope of the line 2x + 3y = -5, we can write that equation in slope-intercept form

 

   2x + 3y = -5

           3y = -2x - 5

             y = (-2/3)x = 5/3

 

The slope of the above line is -2/3.

The slope of the line perpendicular to this line has a slope that is the negative reciprocal.

The slope of the perpendicular line is 3/2.    NOTE:  product of the slope of perpendicular lines, is -1

 

So we are looking for the equation of the line with slope 3/2, that passes through (-6, 1).

 

Using the point-slope formula,

 

     y - y₁₌ m(x - x₁)

 

     y - 1 = (3/2)(x - -6)

     y - 1 = (3/2)(x + 6)

     y - 1 = (3/2)x + 9

          y = (3/2)x + 10

 

The equation of the line is y = (3/2)x + 10

 

We can plug in point (-6,1) to confirm that it is on the line.

 

    1 = (3/2)(-6) + 10

    1 = -9 + 10

    1 = 1

 

Answer 3

First, you need to determine the slope of the equation 2x + 3y = -5. To do that, you simply solve for y which would give you y = -2/3x - 5/3. This is in the slope-intercept form, thereby giving you a slope of -2/3.

 

The slope of lines that are perpendicular to each another will be the negative inverse of each other. The inverse of -2/3 is -3/2, so the slope of the line in question will be the negative of that which equals 3/2.

 

Now, to determine the slope intercept form, you must start with the point-slope form: y - y₁ = m(x - x₁). Substituting gives you y - 1 = 3/2 (x - (-6)). Now, solve for y:

 

y - 1 = 3/2x - (-9)

y - 1 = 3/2x + 9

     y = 3/2x + 10