1. Writing Linear Equations
Using a Slope and a Point or
2 Points

2. Review of Writing Equations
Thus far we have written an equation when given a graph, a table , and a slope and y-intercept. The primary form of linear equation we write is the
_________- _______________ form. In order to write an equation in slope-intercept form we need to have the ___________ and the ___-____________________.
Let’s do a quick review
Slope
intercept
Slope Y
intercept

3. Writing Equations From a Graph
We know our equation is going to look like ___________________. First we find the __________________. In this case it is ______. Next we use the ______ over the ______ to get the ____________. In this case the slope is _____The equation would be •
Y- intercept -1
rise •
run
slope
3/1 = 3

4. Writing Equations from Tables+2
To find the slope from the table we find the ________ in ___ values and place them over the _________ in ___ values . For the table at the right the slope would be _______.
To find the y-intercept we substitute the ___ & ____ values from one of the points in the table into our equation and solve to find the ___-______________.
change Y X 1 3 5 7 Y 9 13
change X +4
4/2 = 2 1 1 X Y -1 Y 2 -1
intercept

5. Writing Equations Given the Slope and a Point
Sometimes we are not given the picture, but only the data in the way of slopes and points. The process is still the same. In order to write the equation we need to have the __________ & ____________________.
Slope
Y-intercept
The point ( 2, 5) is on the line because when the coordinates are substituted into the equation you get a
True
statement
Every point on a line represents a solution to the linear equation. In other words, when you insert the coordinates of the point into the linear equation you will get a ________ statement.
TRUE

6. Writing Equations Given the Slope and a Point (cont.)
To find the equation of a line given the slope and a point you substitute the coordinates and the slope into the equation _________________.
You will notice the only variable you have left to solve for is _____ the __________________.
Write the equation with slope of 4 through the point ( 1 , 7)
___ = ____ (___)+ b
___ = ____ + b
___ = b 7 4 1 7 4 3 b
Y-intercept
So the equation is
Y = ____ X ______ 4 +3

7. Practice 1. Write the equation of the line with m = 2 through (1, -3)
___ = ____ (___) + b
___ = ____ + b
___ = b
Y = ____X _____
2. Write the equation of the line with m = -4 through
(2, 6)
___ = ____ (___) + b
___ = ____ + b
___ = b
Y = ____X _____ -3 2 1 6 -4 2 -3 2 6 -8 -5 14 2 -5 -4
+14
3. Write the equation of the line with m = 1/2 through
(4, 1)
___ = ____ (___) + b
___ = ____ + b
___ = b
Y = ____X _____ 1
1/2 4 1 2 -1
1/2 -1

8. Writing Equations Given 2 Points
The process is very much the same here as it is with the slope and a point except we do not know the ___________. We calculate the ____________ from the 2 points by taking the change in ____ values over the change in ____ values. We then take that value for the slope and use ________ point to find the equation just like we did before.
Find the equation of the line between ( 1, 6) & ( 3, 10) +4 2
slope +2
slope y
___ = ____ (___) + b
___ = ____ + b
___ = b
Y = ____X _____ 6 2 1 x 6 2 4
either 2 +4

9. Practice 4. Write the equation of the line through ( 3, -2) & ( 5, 2 )
___ = ____ (___) + b
___ = ____ + b
___ = b
Y = ____X _____
5. Write the equation of the line through ( -1, 2) & ( 0, -2 )
___ = ____ (___) + b
___ = ____ + b
___ = b
Y = ____X _____ +4 -4 2 -4 +2 +1 -2 2 3 2 -4 -1 -2 6 2 4 -8 -2 2 -8 -4 -2
6. Write the equation of the line through ( 2, -2) & ( 4, 3 )
___ = ____ (___) + b
___ = ____ + b
___ = b
Y = ____X _____ +5
5/2 +2 -2
5/2 2 -2 5 -7
5/2 -7