What is an equation of the line that passes through the point (4,-6) and has a slope of -3?

2 Answers
May 27, 2018

#y=-3x+6#

Explanation:

.

The equation of a straight line has the form:

#y=mx+b# where #m# is the slope and #b# is the #y#-inercept, i.e. where the line crosses the #y#-axis.

Therefore, the equation of this line will be:

#y=-3x+b# because our slope is #-3#.

Now we plug in the coordinates of the given point the line goes through, and solve for #b#:

#-6=-3(4)+b#

#-6=-12+b#

#b=6#

Therefore, the equation is:

#y=-3x+6#

#y=-3x+6#

Explanation:

Slope#=-3# and passes through point #(4,-6)#.

Using the point-slope general formula, of a line,

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

Substitute the coordinates into #x_1# and #y_1#,

#y-(-6)=-3(x-4)#

Simplify,

#y+6=-3x+12#

Subtract #6# from both sides,

#y=-3x+6rarr# answer

Check:

graph{-3x+6 [-10, 10, -5, 5]}
#y=-3x+6#