Algebra 2 – Unit 12 – Graphing & Linear Equations - NEED TO KNOW…..
A. Terminology –
1. Standard Form of the Linear Equation - Ax  By  C
where A & B are coefficients that are integers and C is an integer constant.
2. Slope – Y-Intercept Form of the Linear Equation - y  mx  b
where m = slope and b = y-intercept.
3. Point – Slope Form of the Linear Equation - ( x, y )
where m  slope and ( x1 , y1 ) is a point on the line.
4. Slope – The slope is represented by m.
rise y change in y y2  y1
m



.
run x change in x x2  x1
If m > 0 then the line slants upwards to the right & If m < 0 then the line slants
downwards to the right. If m = 0 then the line is horizontal where the y value does
not change. If m is undefined then the line is vertical where the x value does not
change.
5. X–Intercept - Is the point where the line crosses the x axis. The ordered pair that
corresponds to the X-intercept is (x-intercept , 0).
6. Y-Intercept – Is the point where the line crosses the y axis. It is represented by b.
The ordered pair that corresponds to the Y-intercept is (0 , b).
7. Abscissa – 1st coordinate of the ordered pair (the x value).
8. Ordinate – 2nd coordinate of the ordered pair (the y value).
9. Parallel Lines – Lines that DO NOT intersect. They are represented by the
symbol . If 2 lines are then their slopes are the SAME.
10. Perpendicular Lines – Lines that intersect at a RIGHT ANGLE. They are
represented by the symbol  . If 2 lines are  then their slopes multiplied
together = - 1 ( m1  m2  1 ). One slope is the negative reciprocal of the other.
B. Graphing Linear Equations –
1. There are several methods you can use to graph linear equations:
a. Set up a Table - Solve for y, Make a table to find x & y coordinates,
then Graph the ordered pairs you find.
b. Use the Slope-Y-Intercept form of the linear equation and
rise
Graph the Y-intercept and use m 
to find additional points on the
run
line.
If the rise > 0 then move up the value of the rise from your Y-Intercept
to find your new y value. If the rise < 0 then move down the value of
the rise from your Y-Intercept to find your new y value.
If the run > 0 then move to the right the value of the run from your
new y value to find your new x value. If the run < 0 then move to the
left the value of the run from your new y value to find your
new x value. Plot this new point ( x, y ) and draw the line connecting
the Y-Intercept and the new point ( x, y ) .
c. If you have 2 points then you can just Graph them and draw the line
connecting them.
d. Find the X-Intercept & the Y-Intercept of the line and Graph them and
draw the line connecting them. To find the X-Intercept let y = 0. To
find the Y-Intercept let x = 0.
C. Writing Linear Equations –
1. There are several methods you can use to write a linear equation depending on
the information that you have:
a. Slope Y-Intercept Form - y  mx  b If you have the slope and yintercept then you can substitute them into this form to find the equation.
b. Point Slope Form - y  y1  m( x  x1 ) If you have the slope and a point
on the line then you can substitute them into this form and solve for y to
find the linear equation.
c. Point Slope Form - y  y1  m( x  x1 ) If you have 2 points and no slope
y y
then you need to use the slope formula: m  2 1 to find the slope.
x2  x1
Then pick one of the points and substitute the slope and the point into
the Point Slope Form of a linear equation. Once you perform that
substitution then you solve for y to find the linear equation.
d. Point Slope Form - y  y1  m( x  x1 ) This form can also be used when
you are given Parallel & Perpendicular lines and asked to find equations
of new linear equations. Just identify the new slope that you are being
asked for and then take a point on the new line and substitute into the
Point Slope Form. Once you perform that substitution then you solve
for y to find the linear equation of the line parallel or perpendicular to
the original linear equation.