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