How do you write the equation of a line in slope intercept, point slope and standard form given (4,2) parallel to y=2x+3?

1 Answer
Feb 27, 2016

#(y-2)=2(x-4)# (in point slope forms) or #y=2x-6# (in slope intercept form) or #2x-y-6=0# (in standard form).

Explanation:

The equation of a line in slope intercept form is given as #y=mx+c#, where #m# is the slope of line and #c# is intercept formed by it on #y#-axis.

Point slope form is used to give equation of a line passing through a given point, say #(x_1,y_1)# and slope #m#. It is written as #(y-y_1)=m(x-x_1)#.

Standard form of equation is in the form #ax+by+c=0#.

In the given equation, #y=2x+3# is already in slope-intercept form and its slope is #2#. Slope of any line parallel to it will also be #2#.

To find the equation of a line passing through #(4,2)# with a slope of #2#, we use point slope form ad the equation is given by

#(y-2)=2(x-4)# or #y-2=2x-8# or #y=2x-6# (in slope intercept form) or #2x-y-6=0# (in standard form).