Fact: Take the equation of any non-vertical line. When you solve for $y$, you get something special: the slope intercept form. $$y=mx+b$$
For those already in the know, $m$ is the slope, and $b$ is the y-coordinate of the $y$-intercept.
Example: Write the line $2x+3y=6$ in slope-intercept form.
Example: Graph the line $y=-\frac{2}{3}x+2$ in slope-intercept form.
Example: Use the graph to determine the equation of the line.
Example: Use the given table of values for a linear function to determine the following:
a. Value of $\Delta x$ shown in the table
b. Value of $\Delta y$ produced in the table
c. Slope of this line
d. The y-intercept of this line
e. Equation of this line in slope-intercept form
Another Fun Form: The point slope form. $$y-y_1=m(x-x_1)$$ Example: Write the equation of the line below in point-slope form.
One More Example: Write in slope-intercept form the equation of the line passing through $(2, 3)$ and perpendicular to $y=\frac{3}{7}x-1$