How do you find the "m" and "b" of any linear equation?

1 Answer
Mar 19, 2018

Answer:

#m# is the slope, while #b# is the y-intercept.

Explanation:

Any linear equation has the form of

#y=mx+b#

  • #m# is the slope of the equation

  • #b# is the y-intercept

The slope of the line, #m#, is found by

#m=(y_2-y_1)/(x_2-x_1)#

where #(x_1,y_1)# and #(x_2,y_2)# are the coordinates of any two points in the line.

The y-intercept, #b#, is found by plugging in #x=0# into the equation, which results in #y=b#, and therefore is the y-intercept.

In some cases, if the equation is already arranged for you nicely, like #y=3x+5#, we can easily find the y-intercept for this line, which is #5#.

Other times, the equation might not be arranged nicely, with cases such as #1/2x+3y=5#, in which we solve for the y-intercept:

#1/2x+3y=4#

#3y=4-1/2x#

#y=(-1/2x+4)/3#

#y=-1/6x+4/3#

So, the y-intercept of this line is #4/3#.