Write an equation ​(a) in​ slope-intercept form

Question

ASK A QUESTION

Write an equation ​(a) in​ slope-intercept form and ​(b) in standard form for the line passing through ​(−2,4) and parallel to x+3y=5.

Answer 1

a)

Slope - Intercept form of a Line Equation is y  =  mx + c ------------> (1)

b)

Given line equation

x + 3y  =  5

3y  = - x + 5

y  =  ( - x + 5 ) / 3

y  =  (-1/3) x + 5/3 --------------> (2)

Compare Eq (2) with Eq (1)

Slope m  =  -1/3

The parellel line also has the same slope

Hence,

Substitute the point (x, y) = (-2, 4) and m  =  -1/3  in Eq (1) and find c

4  =  -2(-1/3) + c

4  =  2/3 + c

c  =  4 - 2/3

c  =  (12 - 2) / 3

c  =  10/3

Substitute c = 10/3 and m = -1/3 in Eq (1)

y  = -x/3 + 10/3

y  =  (-x + 10) / 3

3y  =  -x + 10

x + 3y  =  10

Answer :

a)  Slope - Intercept form of a Line Equation is y  =  mx + c 

b) Line parellel to given line is x + 3y  =  10.