How do you write an equation in slope-intercept form for the line that passes through #(4,-2)# and is parallel to the graph of #y=1/2x-7#?

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Answer 1 · 2016-11-19T22:59:02

#y=1/2 x -4#

Equation of line through #(4,-2)# and parallel to #y=1/2 x-7#

The given equation is in the form #y=mx+b#, where #m=#slope.

Parallel lines have equal slopes, so the slope of the line we are trying to find is #m=1/2#.

Next, use the point-slope form of a line:

#y-y_1=m(x-x_1)# where #(x_1,y_1)# is a point on the line.

#y- -2=1/2 (x-4)#

#y+2=1/2 x -2#
#color(white)a-2color(white)(aaaaaa)-2#

#y=1/2 x -4#

OR

Use the slope intercept form of a line (again with #m= 1/2#):

#y=mx+b# where #b=#the #y# intercept.

Plug in #(4,-2)# for #x and y# and solve for #b#.

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

#-2=color(white)(aa^2)2+b#
#-2=-2#

#-4=b#

The equation is then #y= 1/2 x-4#