How do you write the equation of the line that is parallel to y=x+3 and passes through (-4,1)?

2 Answers
Jun 16, 2017

Answer:

#y=x+5#

Explanation:

If one line is parallel to another line, then they have the same slope, #m#, as found in the point slope form

#y-y_1=m(x-x_1)#

Plugging the parallel slope, #m=1# and the point #(-4,1)# gives us

#y-1=1(x-(-4))#

#y-1=x+4#

Adding to #1# both sides

#y=x+5#

Graphing them both at the same time, reveals two separate graphs which have the same slope (i.e., they are parallel). The top graph passes through #(-4,1)#

graph{(y-x-3)(y-x-5)=0}

Jun 16, 2017

Answer:

#y=x+5#

Explanation:

A line parallel to a given line say #ax+by+c=0# is always #ax+by+k=0#, where #k# is another constant. Note that coefficients and signs of #x# and #y# remain same,, while constant is different.

Hence a line parallel to #y=x+3# will have the equation

#y=x+k# and as it passes through #(-4,1)#, we have

#1=-4+k# or #k=4+1=5#

Hence equation of desired line is #y=x+5#

Note #-# Equation of line perpendicular to #ax+by+c=0# is of the type #bx-ay+k=0#. Observe that while coefficients of #x# and #y# are interchanged, sign of only one of them is changed.