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

Question

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

Savannah Anderson · Accepted Answer

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

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

Eva Abramson · Answer

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

Savannah Anderson · Answer

undefined The equation of the line with slope $ m = -\frac{36}{49} $ that passes through the point $ \left(-\frac{6}{7}, \frac{16}{21}\right) $ is:

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

where $ (x_1, y_1) $ represents the given point.

Substituting $ m = -\frac{36}{49} $, $ x_1 = -\frac{6}{7} $, and $ y_1 = \frac{16}{21} $ into the equation:

$$ y - \frac{16}{21} = -\frac{36}{49} \left(x + \frac{6}{7}\right) $$

After simplifying, the equation becomes:

$$ y = -\frac{36}{49}x + \frac{64}{49} $$