SOLUTION: Write an equation for the line in point/slope form and slope/intercept form that passes through (1,4) and parallel to the line 2x-3y=6.

Algebra ->  Linear-equations -> SOLUTION: Write an equation for the line in point/slope form and slope/intercept form that passes through (1,4) and parallel to the line 2x-3y=6.      Log On


   

Question 87381: Write an equation for the line in point/slope form and slope/intercept form that passes through (1,4) and parallel to the line 2x-3y=6.
Answer by checkley75(3666) About Me  (Show Source):
You can put this solution on YOUR website!
FIRST WE NEED TO FIND THE SLOPE OF THE LINE EQUATION THUS:
2X-3Y=6
-3Y=-2X+6
Y=-2X/-3+6/-3
Y=2X/3-2 (RED LINE)WHICH HAS A SLOPE OF 2/3.
ANY PARALLEL LINE MUST ALSO HAVE A SLOPE OF 2/3.
NOW WE REPLACE THE X & Y ITEMS IN THE LINE EQUATION (Y=mX+b) WITH THE POINTS (1,4) & SOLVE FOR THE Y INTERCEPT (b).
4=2/3*1+b
4=2/3+b
b=4-2/3
b=(12-2)/3
b=10/3 FOR THE Y INTERCEPT.
THUS WE HAVE THE EQUATION Y=2X/3+10/3 (GREEN LINE)
PROOF
+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+y+=+2x%2F3+-2%2C+y+=+2x%2F3+%2B10%2F3%29+ (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, of TWO functions y =2x/3 -2 and y = 2x/3 +10/3).