Warm Up #10
1.) Graph 5x + 7y =35
2.) Graph y= 2x -3
Graph 5x + 7y =35
Solve for “y”
7y = -5x +35
Y = -5/7 x + 5
X -values Y= -5/7x +5 Y- values (X, Y)
7 -5/7( 7 )+5 0 (7, 0)
0 -5/7( 0 )+5 5 (0,5)
-7 -5/7 (-7 )+5 10 (-7, 10)
Find 3 points using the table, and graph the line of the equation.
y = 2x - 3
0
1
-1
-1
-3
-5
7.3 Linear Equations and Their
Graphs
Linear Equations
(Graphs are straight lines)
1. Equation is linear only if the each variable has an exponent of “1”.
3 x
1
2. (exponent in denominator is not linear)
3 x
1
3. Products of variables not linear, ie (x)(y) y = 2x + 1 y = x 2 + 1 y – 3x = -7
5y = 14 xy = 2 y
x
2 y
2 x
-6 -4 -2
A
-1
-2
-3
-4
2
1 y
4
3 x - intercept
B
2 4 y - intercept
X
6
Graphing using Intercepts
1) Let x=0 and determine the y-intercept.
2) Let y=0 and determine the x-intercept
3) Plot both points. Connect them with a line.
Graph
4x + 3y = 12 using intercepts
6
Find x-intercept
4x + 3( 0 ) = 12
4x = 12 x = 3
5
4
3
2
Find y-intercept
4( 0 ) + 3y = 12
3y = 12 y = 4
1
-8 -6 -4 -2 2 4 6 8
-1
-2
-3
-4
-5
-6
Graph
2x + 3y = 12 using intercepts
6
5
4
3
2 x y
0
4
6 0
1
-8 -6 -4 -2 2 4 6 8
-1
-2
-3
-4
-5
-6
Graph
3x + 5y = 15 using intercepts
6
5
4
3
2 x y
0
3
5 0
1
-8 -6 -4 -2 2 4 6 8
-1
-2
-3
-4
-5
-6
Graph
5x - 2y = 10 using intercepts
6
5
4
3
2
1 x y
0
5
2 0
6 8 -8 -6 -4 -2 2 4
-1
-2
-5
-6
-3
-4
Graph
2y = 3x - 6 using intercepts
6
5
4
3
2 x y
0
3
2 0
1
-8 -6 -4 -2 2 4 6 8
-1
-2
-3
-4
-5
-6
Horizontal and Vertical Lines
• The graph of y= # is HORIZONTAL
• The graph x =# is VERTICAL
-8
Graph
4y = 16 using 3-points
6
5
4
3
2
1 x y
0
3
6
-6 -4 -2
-1
-2
-3
-4
-5
-6
2 4 6 8
-8
Graph
3x = 18 using 3-points
6
5
4
3
2
1 x y
-6
0
3
- 4
-4 -2
-1
-2
-3
-4
-5
-6
2 4 6 8
Differences between graphing by using a table and graphing by finding the x and y intercepts
• When graphing by a table you need to solve for y (Slope Intercept Form y=mx+b)
• When graphing by finding the x and y intercepts you do not have to solve for y
(Standard Form Ax +By =C)
Assignment
Page 316
( 16 – 42 even and 45-49 all)
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