2.2: linear equations. graphing linear equations y is called the dependent variable because the...
DESCRIPTION
Standard Form Standard form of a linear equation is Ax + By = C, where A, B, and C are real numbers and A, B ≠ 0. Graph linear equations in standard form by finding the x- and y- interceptsTRANSCRIPT
2.2: Linear Equations
-5 -4 -3 -2 -1 1 2 3 4 5
-5
-4
-3
-2
-1
1
2
3
4
5
Graphing Linear Equations• y is called the dependent variable because the value of y depends on x
• x is called the independent variable
4Ex1) Graph the equation 23
y x
y mx b
Will this be a function??
Standard FormStandard form of a linear equation is Ax + By = C, where A, B, and C are real numbers and A, B ≠ 0.
Graph linear equations in standard form by finding the x- and y- intercepts
-5 -4 -3 -2 -1 1 2 3 4 5
-5
-4
-3
-2
-1
1
2
3
4
5
Ex2) 2 4 8x y
1 2 3 4 5 6 7 8 9
1
2
3
4
5
6
7
8
9
More PracticeEx3) The equation 3x + 2y = 120 models the number of passengers who can sit in a train car, where x is the number of adults and y is the number of children. Graph the equation. Explain what the x- and y- intercepts represent. Describe the domain and range.
Point-Slope FormThe line through the point (x1, y1) with slope m has the equation
y – y1 = m(x – x1)
Ex6) Write in standard form an equation of the line with1slope through the point ( 6,2).3
Point-Slope FormThe line through the point (x1, y1) with slope m has the equation
y – y1 = m(x – x1)
Ex7) Find the equation of a line through the points (-2, 3) and (1, 6). Then write it in standard form.
Slope-Intercept Form
y = mx + bEx8) What is the slope of the line 4x + 6y = 18?
What is the slope of:
a horizontal line?
a vertical line?
parallel lines?
perpendicular lines?
-6 -5 -4 -3 -2 -1 1 2 3 4 5 6
-6-5-4-3-2-1
123456
Perpendicular LinesEx9) Write an equation of the line through (5, –3) and perpendicular to y = 4x + 1. Graph both lines.
Exit Problems:1. Determine the slope, and the x- and y- intercepts of each of
the functions2. Write the equation in both standard and y-intercept form3. Graph the equations
Exit Problems:1. Determine the slope, and the x- and y- intercepts of each of
the functions2. Write the equation in both standard and y-intercept form3. Graph the equations
Exit Problems:1. Determine the slope, and the x- and y- intercepts of each of
the functions2. Write the equation in both standard and y-intercept form3. Graph the equations
Special Lines:
Special Lines:
2.2: Linear Equations
Our greatest glory is not in never falling, but in getting up every time we do.
Homework #10
Pg 67 # 2-14 even, 20 – 34 even, 37, 42, 54