Slope-Intercept Form

Key Questions

How do you find the "m" and "b" of any linear equation?
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#.
Nam D. · 1 · Mar 19 2018
How do you determine the slope and y intercept when given a graph?

The #y#-intercept #b# can be found by reading the #y#-axis where the graph hits the y-axis, and the slope #m# can be found by finding any two distinct points #(x_1,y_1)# and #(x_2,y_2)# on the graph, and using the slope formula below.

#m={y_2-y_1}/{x_2-x_1}#.

I hope that this was helpful.

Wataru · 2 · Oct 29 2014
What is Slope-Intercept Form?

Answer:

#y = mx + b#

Where:
#m# is the slope of the line.
#b# is the y-intercept of the line.

Explanation:

Consider #y = x#

graph{y=x [-10, 10, -5, 5]}

In this equation, the coefficient to #x# is 1 and our y-intercept is 0.

We could think of that equation as looking like:

#y = 1x + 0#

Notice that the graphed line has a "rise-over-run" of #1/1# which is just 1 and the line passing through the y-axis at #y=0#

Matt B. · 1 · Apr 5 2018