Line L has equation #2x- 3y=5#. Line M passes through the point (3, -10) and is parallel to line L. How do you determine the equation for line M?

1 Answer
Jun 15, 2017

Answer:

See a solution process below:

Explanation:

Line L is in Standard Linear form. The standard form of a linear equation is: #color(red)(A)x + color(blue)(B)y = color(green)(C)#

Where, if at all possible, #color(red)(A)#, #color(blue)(B)#, and #color(green)(C)#are integers, and A is non-negative, and, A, B, and C have no common factors other than 1

#color(red)(2)x - color(blue)(3)y = color(green)(5)#

The slope of an equation in standard form is: #m = -color(red)(A)/color(blue)(B)#

Substituting the values from the equation into the slope formula gives:

#m = color(red)(-2)/color(blue)(-3) = 2/3#

Because line M is parallel to line L, Line M will have the same slope.

We can now use the point-slope formula to write an equation for Line M. The point-slope formula states: #(y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))#

Where #color(blue)(m)# is the slope and #(color(red)(x_1, y_1))# is a point the line passes through.

Substituting the slope we calculated and the values from the point in the problem gives:

#(y - color(red)(-10)) = color(blue)(2/3)(x - color(red)(3))#

#(y + color(red)(10)) = color(blue)(2/3)(x - color(red)(3))#

If necessary for the answer we can transform this equation to the Standard Linear form as follows:

#y + color(red)(10) = (color(blue)(2/3) xx x) - (color(blue)(2/3) xx color(red)(3))#

#y + color(red)(10) = 2/3x - 2#

#color(blue)(-2/3x) + y + color(red)(10) - 10 = color(blue)(-2/3x) + 2/3x - 2 - 10#

#-2/3x + y + 0 = 0 - 12#

#-2/3x + y = -12#

#color(red)(-3)(-2/3x + y) = color(red)(-3) xx -12#

#(color(red)(-3) xx -2/3x) + (color(red)(-3) xx y) = 36#

#color(red)(2)x - color(blue)(3)y = color(green)(36)#