Linear Functions, Slope, Intercepts, and Slope Calculation
Explore linear functions, slope calculations, intercepts, and determining slopes through points in this comprehensive guide. Learn how to find values, understand domains and ranges, identify functions, and interpret the mathematical concepts of rise over run. Practice solving examples to enhance your understanding.
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Presentation Transcript
Find the indicated value 1) g(-5) if g(x) = 3x - 2
Find the domain and range 2) {(3, 4), (3, 5), (5,6), (6,7)}
Determine which are functions 3) 4) 5)
Chapter 2 Section 4 Linear Functions and Slope All graphs need to be done on graph paper. Four, five squares to one inch is the best. One unit = one square
Definition x intercept of the graph: x-coordinate where the graph intersects the x-axis Ordered pair: (x, 0) y intercept of the graph: y-coordinate where the graph intersects the y-axis Ordered pair: (0, y)
Example Find the x and y intercept. y x
Find the x, y intercepts a) x+ 3y = 6 b) 3x = 5y - 15
Slope of a line How steep is the line. Where do you find slope? Roof of a house pitch Highway to Tahoe grade What other examples?
Mathematical Definition Slope Graph: rise over run: ???? ??? Computation: ?2 ?1 ?2 ?1 ? ???? ?? ? ? ???? ?? ?
Example Find slope: y x
Slope Find the slope of a line that passes through (-2, 0) and (1, 4)
Find the slope that passes through the two points. c) (- 1 , 4) and (2, 5) d) (-3, - 4) and (-1, 6)
Slope Positive slope: rises Negative slope: fall Zero slope: horizontal No slope: vertical
Slope-Intercept Form Nonvertical line with slope, m, and y-intercept, b. y = mx + b
Find the slope and y-intercept e) y = 3x - 2 3 4x+2 f) f(x) = ? ?
Rewrite in slope-intercept form g) 5y = 4x + 2 h) 7x + 2y = 14
Standard form Nonvertical line where a 0 and a, b, c are real numbers ax + by = c
Rewrite in standard form i) f(x) = -3x + 2 3 5x+6 j) f(x) = ? ?
Sketch the graph k) 5y = 4x l) 5x + 3y = 15
