Linear Functions

Linear Functions - m and the y-intercept (0, b ). Use the...

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2.3 - Linear Functions Definition of a Linear Function A linear function of x is of the form f ( x ) = mx + b , m 0 where m and b are real numbers. The slope of the line is the steepness, or rate of change between any two points on the line. x y P1 P2 x1 x2 y1 y2 rise run Slope Formula The slope m of the line passing through the points P 1 x 1 , y 1 and P 2 x 2 , y 2 with x 1 x 2 is given by m = y 2 - y 1 x 2 - x 1 Example: Find the slope of the line passing through the given points. (3, 4) and (1, -2) Solution. m = y 2 - y 1 x 2 - x 1 = -2 - 4 1 - 3 = -6 -2 = 3. x y (3, 4) (1, -2)
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Find the slope of the line passing through the given points. (-4, -3) and (1, -2) (-2, 5) and (7, 5) (-6, -8) and (-6, 5) Horizontal and Vertical Lines The graph of x = a is a vertical line through ( a , 0). x y (a, 0) The graph of y = b is a horizontal line through (0, b ). x y (0, b)
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Slope-Intercept Form The graph of f ( x ) = mx + b is a line with slope
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Unformatted text preview: m and the y-intercept (0, b ). Use the slope-intercept form to graph the equation. f ( x ) = -2 x + 5 x-10-5 5 10 y 10 5-5-10-3 x + 12 y = -24 x-10-5 5 10 y 10 5-5-10 Point-Slope Form The graph of y- y 1 = m ( x- x 1 ) is a line that has slope m and passes through ( x 1 , y 1 ). Therefore, we can write the equation of a line provided we know its slope and at least one point on the line. Find the equation of the line with the given slope passing through the given point. Slope 2 3 ; through (-3, 4) Find an equation of the line through the given points. Write the equation in the form y = mx + b . Through (-1, 1) and (2, -4)...
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Linear Functions - m and the y-intercept (0, b ). Use the...

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