Review of Graphing

Warm up

Solve for y

1) 1-5y=-14

-5y=-14

-5y=-15

-5y-5=-15-5

y=3

2) 3x+2y-4=0

2y=0

2y=-3x+4

2y2=-3x+42

y=-32x+42

y=-32x+2

y=mx+b

m – slope, y – intercept

Review of Graphing

Example 1: Sketch 2x-y-1=0 using the slope and y-intercept

Solution:

Write 2x-y-1=0 in the form, y=mx+b.

2x-y-1=0

2x-1=y

y=2x-1

y-int. is -1 (b=-1)

slope is 2 (m=2)

1. Plot the y-int.
2. Use the slope to get a second.

m=2

=2/1 point (1,1)

Or

=-2/-1 point (-1,-3)

3. Join the y-int. and the second with a straight line.

Example 2: Sketch 2x-3y=12 using the x and y-intercepts.

Solution:

x:0,6

y:-4,0

y-int.: let x=0

2(0)-3y=12

-3y=12

-3y-3=12-3

y=-4

So, y-int. is -4, as a point (0,-4)

x-int.: Let y=0, 2x-300=12

2x=12

2×2=122

x=6

So, the x-int. is 6, as a point (6,0)

Example 3: Is the point (3,1) on the line y = 4x + 10?

Solution: x=3,y=1. Check the L.S. and the R.S.

L.S.=y

=1

R.S.=-4x+10

=-4(3)+10

=-12+10

=-2

Point (3,1) is not on the line y=-4x+10

Since L.S. neq R.S.

Example 4: Sketch using a table of values.

y=-x2+3

For x=-2

y=–22+3

=-4+3

=-1

Identify the y-intercept, vertex and axis of symmetry

y-int=3

vertex: (0,3)

A.O.S: x=0

Summary of Characteristics