Transcript 3-4 The Graph of Ax + By = C

On a quiz show, 30 points are given for correct
answers to Regular questions, and 60 points are
given for correct answers in the Bonus round.
Let R represent the number of regular questions
answered correctly and B represent the number
of bonus questions answered correctly.
a)
Write an expression that give the total number of points
earned.
30R + 60B
b)
c)
Suppose a contestant earned 900 points. Write an
equation relating R, B, and the number of points earned.
30R + 60B = 900
If the contestant answered 20 regular questions correctly
and earned 900 points, how many bonus questions were
answered correctly?
5 Bonus Questions
d)
Find another possible solution to the equation in b.
3-4
The Graph of
Ax + By = C
Standard Form
Ax + By = C
• A has to be POSITIVE!!!
• A and B can not be FRACTIONS or
DECIMALS!!!
• A and B can not BOTH be zero.
• The graph of Ax + By = C, where A and B are
not both 0, is a line.
Finding Useful Information
Standard Form : Ax + By = C
-To find the x-intercept:
• Substitute 0 in for y.
• Solve for x
• x=C/A
-To find the y-intercept:
• Substitute 0 in for x.
• Solve for y
• y=C/B
-To find slope:
• Subtract Ax
• Divide by B
• m = -A / B
Example
4/8/2016
Give an equation in Standard Form
for the line with y-int of – 5 and
slope 3 . Identify the x-int.
4
Ax  By  C ←Standard Form→3 x  4 y  20
3
y  x 5
4
3
 x  y  5
4
3
 4( x  y  5)
4
20
x  int 
3
y  int  5
Example
4/8/2016
Give an equation in Standard Form
for the line with y-int of 7 and
slope  1 . Identify the x-int.
5
Ax  By  C
1
y   x7
5
1
x y 7
5
1
5( x  y  7)
5
←Standard Form→
x  5 y  35
x  int  35
y  int  7
4/8/2016
Complete the Table
Standard Form
Ax + By = C
5x – 10y = 30
2x + 5y = 20
6x – 7y = –42
x=–9
Slope
y-intercept
x-intercept
–3
6
–2/5
4
10
6/7
6
–7
1/2
undefined
none
–9
Graphing by Intercepts
To Graph by Intercepts
• Find x-intercept
• Plot on Graph
• Find y-intercept
• Plot on Graph
• Draw line through the
points
4x + 3y = 12
4x + 3(0) =12
4x + 3y = 12
x-int = 3 4(0) + 3y = 12
y-int = 4
4/8/2016
Graphing by Intercepts
Graph the equation:
6x – 4y = 24
using its intercepts.
x-int = ?
6x – 4(0) =24
x-int = 4
(4, 0)
y – int = ?
6(0) – 4y =24
y-int = –6
(0, –6)
Assignment
• Lesson Master 3-4
• Pages 160-161 #’s 6, 8, 9,12-18, 20-22.
• Study for Quiz on Sections 3-1 to 3-3!!!!!