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Name the domain and range for the relation shown in each graph
D = {x | x is a real number}
R = {y | y ≥ -2}
D = {x | x is a real number}
R = {y | y ≥ 0}
Which of these represent linear functions?
linear
nonlinear
linear
nonlinear
In a linear equation, each term is either a constant or the product of a constant and (the first power of) a single variable.
Slope-intercept form
y = mx + b
f(x) = mx + b
m is the slope of the line
b is the y-intercept
What are the slope and y-intercept of the line ? Slope = 3
y-intercept = -9
Graph the line y-intercept = -9
Slope = 3
Slope = Δy Δx
The graph of a linear equation is a line.
Standard form Ax + By = C
• A, B and C are integers (not fractions!)
• A is positive
• A and B are not both zero
3x + 5y = -2 is in standard form
Write the equation in standard form. Identify A, B, and C.
Ax + By = C
Simplified?
2 2 2
Write the equation in standard form. Identify A, B, and C.
Simplified?
Ax + By = C
Write the equation in standard form. Identify A, B, and C.
Simplified?
Ax + By = C
-3 (-3)
Find the x- and y- intercepts of -2x + y – 4 = 0
x-intercept
-2x + 0 – 4 = 0
-2x – 4 = 0
-2x = 4
x = -2
The x-intercept is -2
(-2, 0)
y-intercept
-2(0) + y – 4 = 0
0 + y – 4 = 0
y – 4 = 0
y = 4
The y-intercept is 4
(0, 4)
x-intercept : –2
y-intercept: 4
(0, 4)
(–2, 0)
Graph -2x + y – 4 = 0