Lesson 34 Graphing linear equations 2 Linear function

Lesson 34 Graphing linear equations 2

Linear function • A function with a constant rate of change is called a linear function. • Every non-vertical line represents a linear function. • To determine whether a graph is the graph of a function, you can use the vertical line test.

Identifying graphs of linear functions • • • To determine if a graph represents a linear function, find the rate of change between sets of points. If the rate of change stays the same , it is a linear function. The vertical line test alone does not always tell if a graph represents a function. A curved line could pass the vertical line test , but not have a constant rate of change.

3 common forms of linear equations • Standard form • Slope-intercept form y = mx+b m is the slope and b is the yintercept • Point-slope form y-y 1=m(x-x 1) m is the slope and (x 1, y 1) is a point the line on Ax + By + C A and B are both not 0

Graphing given standard form • • • You can make a table of values or Use x-intercept and y-intercept or Change to slope-intercept form

examples • x+3 y = 12 • -3 x+4 y = -4 • -2 x + 5 y = -20 • 3 x + 2 y = 12

Graphing given point-slope form • • • Graph y-3=-1/2 (x+2) Point slope form y-y 1= m(x-x 1) So y 1 = 3 , m = -1/2 , x 1= -2 Point on the line is (x 1, y 1) = (-2, 3) Plot this point and then use the slope to find another point on the line

Parent function • • • The most basic linear function is y= x All other linear functions are transformations of y = x

Transformations of f (x) = x • • • -f(x) is a reflection over the x -axis f(x) + c is a vertical shift c units up, if c is positive, f(x) + c is a vertical shift c units down, if c is negative c f(x) is a vertical stretch by a factor of c , if c>1 c f(x) is a vertical compression by a factor of c , if 0<c<1 See examples p. 248

Horizontal and vertical lines • Let b be any constant • y = b is a linear function, whose graph is a horizontal line (it crosses the y-axis) and has a slope of 0 x= b is not a function, it is a vertical line with an undefined slope (it crosses the xaxis) •