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)
- Plot the y-int.
- Use the slope to get a second.
m=2
=2/1 point (1,1)
Or
=-2/-1 point (-1,-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
