What is the equation of the line with slope m= 14/25 m=1425 that passes through (23/5, (-23)/10) (235,2310)?

1 Answer
May 7, 2016

y = (14x)/25 + 4 219/250y=14x25+4219250

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)(yy1)=m(xx1)
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)(yy1)=m(xx1)

(y - (-23/10)) = 14/25(x - 23/5)(y(2310))=1425(x235)

y + 23/10 = (14x)/25 - 14/25 xx23/5 " " xx250y+2310=14x251425×235 ×250

250y + 250xx23/10 = 250xx(14x)/25 - 250xx14/25 xx23/5250y+250×2310=250×14x25250×1425×235

250y + 575 = 140x - 28 xx23250y+575=140x28×23

250y = 140x + 1219250y=140x+1219

y = (14x)/25 + 4 219/250y=14x25+4219250

Method 2 uses y = mx + cy=mx+c

Subst for m, x and ym,xandy to find cc

(-23/10) = 14/25 xx 23/5 + c " " xx 250(2310)=1425×235+c ×250

250xx(-23/10) = 250xx14/25 xx 23/5 + 250c250×(2310)=250×1425×235+250c

-575 = 644 + 250c575=644+250c

1219 = 250c1219=250c

c = 1219/250 = 4 219/250c=1219250=4219250

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

y = (14x)/25 + 4 219/250y=14x25+4219250.