What is the equation of the line with slope # m= -36/49 # that passes through # (-6/7, 16/21) #?

2 Answers
May 4, 2017

#y=-36/49x+1432/1029# or

#y=-36/49x+1 403/1029#

Explanation:

#y-y_1=m(x-x_1)#

From the question, we get the following information:

#m=-36/49,#

#x_1,y_1=(-6/7,16/21)#

The point slope equation.

#y-16/21=-36/49(x-6/7)#

Simplify.

#y-16/21=-36/49x+216/343##lArr# Multiplying two negatives gives a positive result.

Add #16/21# to both sides.

#y-color(red)cancel(color(black)(16/21))+color(red)cancel(color(black)(16/21))=-36/49x+216/343+16/21#

Simplify.

#y=-36/49x+216/343+16/21#

When adding fractions, the denominators must be the same. The Least Common Denominator (LCD) can be found by factoring the denominators.

Prime factorize the denominators #343# and #21#.

#343:##7xx7xx7#

#21:##3xx7##

#"LCD"=3xx7xx7xx7=1029#

Multiply each fraction by the equivalent fraction that will result in the LCD #1029#. An equivalent fraction is equal to #1#, such as #2/2=1#.

#y=-36/49x-(216)/(343)xxcolor(red)(3/3)+16/21xxcolor(green)(49/49)#

Simplify.

#y=-36/49x+(648)/(1029)+(784)/(1029)#

Simplify.

#y=-36/49x+1432/1029# or

#y=-36/49x+1 403/1029#

May 4, 2017

#y = -36/49x + 136/1029#

Explanation:

Use the slope - intercept equation:# y = mx + b#

#y = -36/49 x + b#

Put the point #(-6/7, 16/21)# into the equation as #x " and " y#:

#16/21 = -36/49 * -6/7 + b#

#16/21 = 216/343 + b#

#b = 16/21 - 216/343#

Find a common denominator: #21 = 3 * 7; 343 = 7^3#

Common denominator # = 3 * 7^3 = 1029#

#b = 16/21 * 49/49 - 216/343 * 3/3 = 784/1029 - 648/1029 = 136/1029#

#y = -36/49 x + 136/1029#