SOLUTION: Which is an equation of the line that is parallel to 7x+2y=6 and passes through the point(2,3)?

Algebra ->  Linear-equations -> SOLUTION: Which is an equation of the line that is parallel to 7x+2y=6 and passes through the point(2,3)?      Log On


   



Question 1128211: Which is an equation of the line that is parallel to 7x+2y=6 and passes through the point(2,3)?
Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.
Any line parallel to the given line has the form


    7x + 2y = c,


where "c" is some constant.  For your case, you determine the value of the constant term "c" from the condition,

that the point (2,3) belongs to this line.


For it, substitute the coordinates of the given point x= 2 and y= 3 into the equation (1). You will get


    c = 7*2 + 2*3 = 14 + 6 = 20.


So, your equation is 


    7x + 2y = 20.

Completed and solved.

------------------

To wider your horizon, look into my lessons
    - Find the slope of a straight line in a coordinate plane passing through two given points
    - Equation for a straight line having a given slope and passing through a given point
    - Solving problems related to the slope of a straight line
    - Equation for a straight line in a coordinate plane passing through two given points
    - Equation for a straight line parallel to a given line and passing through a given point
    - Equation for a straight line perpendicular to a given line and passing through a given point
in this site.


Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Which is an equation of the line that is parallel to 7x%2B2y=6 and passes through the point(2,3)?
parallel lines have same slope
so, first find a slope of 7x%2B2y=6
2y=-7x%2B6
y=-7x%2F2%2B6%2F2
y=-%287%2F2%29x%2B3=> slope is -%287%2F2%29
and, parallel line is
y-y%5B1%5D=m%28x-x%5B1%5D%29......use point (2,3)
y-3=-%287%2F2%29%28x-2%29
y-3=-%287%2F2%29x-2%28-%287%2F2%29%29
y-3=-%287%2F2%29x%2B7
y=-%287%2F2%29x%2B7%2B3
y=-%287%2F2%29x%2B10