What is the equation of the line which is parallel to the line 3x +4y =6 and passes through (2, 1)?

Show work and explain please.

1 Answer
Dec 1, 2017

Answer:

#y=-3/4x+5/2#

Explanation:

.
#3x+4y=6#

Let's solve for #y# so we can have the equation in standard slope-intercept form:

#4y=-3x+6#

#y=-3/4x+3/2#

This is in the form of:

#y=mx+b# where #m# is slope and #b# is the #y#-intercept which is where the line crosses the #y#-axis. Comparing the two we see that:

#m=-3/4# and #b=3/2#

For a line to be parallel to this line, it would have to have the same slope, i.e. its equation would be:

#y=-3/4x+b#

Now, we can use the coordinates of the point the line goes through and plug them into this equation to solve for #b#:

#1=-3/4(2)+b#

#1=-3/2+b#

#b=1+3/2=2/2+3/2=5/2#

Therefore, the equation of the line is:

#y=-3/4x+5/2#