1. Cartesian Grid Plotting Pointsy
Cartesian Grid Plotting Points B
points are ordered pairs, x first, then y, in order
Point (x, y) A D x
A(4, 6) G
B(0, 7)
C(-4, -9) F
D(3, 0)
E(7, -10) C E
F(1.5, -6.5)
G(-3/2, -7/4)
plotting points

2. x y -3 1 -2 4 1 10 7 y graphing using a table of values x-3 1 -2 4 1 10 7
table graph x-3

3. x y -7 1 -5 5 3 7 7 y graphing using a table of values 2 x-7
2(0) - 7 = -7 1 -5
2(1) - 7 = -5 5 3
2(5) - 7 = 3 7 7
2(7) - 7 = 7
table graph 2x-7

4. x y -2 10 6 5 -4 6 -6 y graphing using a table of values 3 x
-2(-2)+6 = 10 6
-2(0)+6 = 6 5 -4
-2(5)+6 = -4 6 -6
-2(6)+6 = -6
table graph –2x+6

5. x y -2 5 4 5 1.5 8 y graphing using a table of values 4 x -1/2(-2)+4=54
-1/2(0)+4 = 4 5
1.5
-1/2(5)+4=1.5 8
-1/2(8) + 4 = 0
table graph
table graph –2x+6

6. 10 6 y x Features of graphed line x-intercept (3, 0) y-intercept 5
SLOPE: the slope of a line is how quickly it rises or falls. The direction!
this line rises 5 every time it steps 3 right
the slope is 5/3
x-intercept
(3, 0) 10 x
y-intercept
(0, -5) 5 3 6
or you could say it is 10/6 which is really 5/3
x-intercept: the point where the line crosses the x-axis; in this case (3, 0).
y-intercept: the point where the line crosses the y-axis; in this case (0,-5).
slope

7. y x Graph equation without a table 8 EXAMPLE: y-intercept
A line can be written in the form:
y = mx + b; where m and b are given numbers.
the b is the ‘y-intercept’
the m is the ‘slope’
it makes it easy to graph without a table x 8
EXAMPLE:
graph y = 2x – 8
y-intercept
(0, -8) 2 1 4
plot the y-intercept (0, -8)
Plot another point or two using the slope, the rise per run right, of 2/1 or 4/2 or 8/4, etc
hint: convert the slope into a fraction
slope-intercept form

8. y 8 x Graph equation without a table 4 y-intercept (0, 6) EXAMPLE:
A line can be written in the form:
y = mx + b; where m and b are given numbers.
the b is the ‘y-intercept’
the m is the ‘slope’
it makes it easy to graph without a table 4 1
y-intercept
(0, 6) 2 8 x
EXAMPLE:
graph y = -2x + 6
plot the y-intercept (0, 6)
Plot another point or two using the slope, the rise per run right, of -2/1 or -4/2 or -8/4, etc
hint: a rise of –2 is a drop of two
slope intercept2

9. y 5 8 x Graph equation without a table y-intercept (0, 2) EXAMPLE:
A line can be written in the form:
y = mx + b; where m and b are given numbers.
the b is the ‘y-intercept’
the m is the ‘slope’
it makes it easy to graph without a table
y-intercept
(0, 2) 5 8 x
EXAMPLE:
plot the y-intercept (0, 2)
Plot another point using the slope, the rise per run right, of 5/8.
slope intercept 3

10. Graphing equations in the slope and intercept form; y = mx + b is easy
But sometimes the x and the y are on the same side of the equals sign;
ax + by = c ; where a, b, and c are given numbers.
There are two ways to graph these:
do a literal conversion to the y = mx + b slope and intercept form; or
do the intercept-intercept method
general form

11. Convert 2x + 4y = 12 subtract 2x from both sides
divide both sides by 4
We tend to write the terms with variables in them first; so:
literal conversion

12. intercept-intercept methody
Plot equation from General form
2x + 4y = 12 x y 3 x 6
Evaluate for x = 0
2(0) + 4y = 12
4y = 12 y = 12/4 = 3
So (0, 3) is one point ; it is on the y-axis
Evaluate for y = 0
2x + 4(0) = 12
2x = 12 x = 12/2 = 6
So (6, 0) is one point; it is on the x-axis
intercept-intercept method

13. Plot equation from General formy
Plot equation from General form
of course, you can evaluate the x or y for any values you want, but zeros are way easier to calculate. And intercepts are easy to plot too
x – 3y = 9 x y -3 x 9
Evaluate for x = 0
(0) – 3y = 9
-3y = 9 y = 9/-3 = -3
So (0, -3) is one point ; it is on the y-axis
Evaluate for y = 0
x – 3(0) = 9
x = 9 x = 9
So (9, 0) is one point; it is on the x-axis
intercept-intercept2