Download Section 2.2

Algebra 2CP
Day 8
2.2 Linear Equations
o Daily Openers
o Check homework
2.2 Linear Equations
linear function – function whose graph is a line.
linear equation – ex. y  4 x  9
 The value of y depends on the value of x, 
dependent variable – y variable
independent variable – x variable
x-intercept – point where the graph crosses the x-axis.
– to find it, let y = 0, and solve for x.
y-intercept – point where the graph crosses the y-axis.
– to find it, let x = 0, and solve for y.
Ex. Find the x-intercept and y-intercept.
4x – 7y – 28 = 0
Ex. Find the x-intercept and y-intercept.
y = ⅔x – 9
SLOPE-INTERCEPT FORM OF A LINE
y  mx  b , where m is the slope of the line and b is the y-intercept.
Ex. Identify the slope and y-intercept:
4
x9
5
y  7 x  8
Ex. Identify the slope and y-intercept:
3 x  8 y  16
Ex. Identify the slope and y-intercept:
20 y  45 x  80
Ex. Identify the slope and y-intercept.
y
Ex. Write a linear equation with slope of 5 and y-intercept of -12
Ex. Write a linear equation with m = ⅝ and y-intercept of (0, 2.5)
Ex. Graph: y 
2
x 1
5
Ex. Graph: 6 x  8 y  20  4
Ex. A waiter makes $3.35 per hour, and 15% of sales in tips. Write an equation that
relates his pay (P) in terms of sales (s).
Ex. Write a linear equation for the graph of the function.
(a)
(b)
STANDARD FORM OF A LINE
Ax  By  C , where A and B are nonzero
Ex. Write the equation in standard form using integers: y  7 x  8
Ex. Write the equation in standard form using integers: y  6  4 x
Ex. Write the equation in standard form using integers: y 
2
x5
3
Ex. Write the equation in standard form using integers: y  
3
1
x
4
3
Ex. Find the x and y-intercept of: 6 x  8 y  48
Ex. Find the x and y-intercept of:  5 x  3 y  30
Ex. Find the x and y-intercept of:  250 x  125 y  500
 TWO POINTS DETERMINE A LINE!
Ex. Graph:  4 x  9 y  72 using intercepts.
Ex. Graph: 50 x  75 y  525 using intercepts.
 Horizontal Line – in the form, y = a
 Vertical Line – in the form, x = b
Ex. Graph the line: x = -3
Ex. Graph the line: y = 5
POINT-SLOPE FORM OF A LINE
y  y1  mx  x1  ,
where (x1, y1) is the point the line passes through, and m is the slope.
Ex. Write an equation of a line that has a slope of 6 and passes through the point (3, -4).
Ex. Write an equation of a line that has a slope of 8/5 and passes through the point (0, 3).
Ex. Write an equation of a line that has a slope of -¾ and passes through the point (-2, -7).
Ex. Write an equation of a line that has a slope of 0 and passes through the point (9, 10).
Ex. Graph the equation: y  6 
4
x  10
5
Ex. Write an equation in point-slope form for the line passing through the two points:
(4, 3) and (2, 9)
Ex. Write an equation in point-slope form for the line passing through the two points:
(2, 3) and (-1, -5)
Ex. Write an equation in point-slope form for the line passing through the two points:
(-6, -7) and (2, -3)
Ex. Is the relationship linear? If so, model the data with an equation.
x
y
-2
7
0
-1
2
-9
5
-21
Homework – pages 67–69 #1–79 odd, 82, 83
Daily Openers – 1. Is the relation a function? {(2, -4), (0, 11), (3, 3), (4, -5), (3, -4)}
2. Find the (a) domain of #1, and (b) range of #1.
1 2
x  8 x  17 , find f (5)
10
4. If f ( x)  x 2  3x  6 , and h( x)  2 x  4 , then find f (h( x)) .
3. For the function: f ( x) 
(a)
5. Determine whether or not the graph is a function.
(b)
(c)