What is the equation of the line with slope # m= 14/25 # that passes through # (23/5, (-23)/10) #?

1 Answer
May 7, 2016

# y = (14x)/25 + 4 219/250#

This is a somewhat unrealistic question, and becomes an exercise in arithmetic rather than maths.

Explanation:

There are 2 methods:

Method 1 . uses the formula #(y - y_1) = m(x - x_1)#
This is great to use if you know the slope (m) and one point, which is exactly what we have here. It involves one step of substitution and a bit of simplifying.

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

#(y - (-23/10)) = 14/25(x - 23/5)#

#y + 23/10 = (14x)/25 - 14/25 xx23/5 " " xx250#

#250y + 250xx23/10 = 250xx(14x)/25 - 250xx14/25 xx23/5#

#250y + 575 = 140x - 28 xx23#

#250y = 140x + 1219#

# y = (14x)/25 + 4 219/250#

Method 2 uses # y = mx + c#

Subst for #m, x and y# to find #c#

#(-23/10) = 14/25 xx 23/5 + c " " xx 250#

#250xx(-23/10) = 250xx14/25 xx 23/5 + 250c#

#-575 = 644 + 250c#

#1219 = 250c#

#c = 1219/250 = 4 219/250#

This leads to the same equation, using values for m and c.

# y = (14x)/25 + 4 219/250#.