4.2 Graphing Linear Functions Use tables and equations to graph linear functions. Parent Functions A family of functions is a group of functions with common characteristics. Simplest function with these characteristics is called a parent function. The linear parent function is y = x or f(x) = x Linear Equation Models a linear function Variable cannot be raised to a power other than 1 y = 2x is linear but y = x2 and y = 2x are not. The y-intercept is the y-coordinate of a point where the graph crosses the y-axis. Slope-Intercept Form For linear equations that are not vertical. Remember, the slope of a vertical line is undefined. Ex: identify the slope and y-intercept for the linear equation y = 5x – 2 Slope: 5 y-intercept: -2 Writing an Equation What is the equation of the line with a 4 slope of − and y-intercept 7? 5 Plug into slope-intercept form: ◦ ◦ 4 m=− 5 4 y=- 5 and b = 7 +7 From a Graph Crosses the y-axis at -2 so b = -2 Pick two points to find the slope: (0, -2) and (1, 0) m=2 Write an equation using slope-intercept form: ◦ y = 2x – 2 From Two Points Find the equation of the line that passes through (2,1) and (5, -8) Use the points to find slope ◦ m = -3 Use slope and one of the points to find b y = -3x + b and plug in the point (2, 1) 1 = -3(2) + b 1= -6 + b 7=b Write the equation ◦ y = -3x + 7 Graphing What is the graph of y = 2x – 1? Practice What is the graph of each linear equation? y = -3x + 4 y = 4x – 8

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# 5.3 Slope-Intercept Form