University:
High School
Course:
High School Geometry
Academic year:

2022
Views:

293

Pages:

4
Author:

Karen Cantrell

NOTES Graphing Linear Equations REVIEW A. CONCEPTS Slope: Describes the steepness of a linear function. m = (y2 - y1) / (x2 - x1) = Δy / Δx = change in y / change in x Positive Slope: The line rises (increases) from left to right. Negative Slope: The line falls (decreases) from left to right. Slope of 0: The line is horizontal. y = number Undefined Slope: The line is vertical. x = number Slope-Intercept Form: y = mx + b where m = slope and b = y-intercept (where the graph crosses the y-axis). B. EXAMPLES Find the slope. a) XY: (-3, 10), (-6, 13), (-9, 16) m = (13 - 10) / (-6 - (-3)) = 3 / -3 = -1 b) XY: (2, 2), (4, 2), (6, 2) m = (2 - 2) / (4 - 2) = 0 / 2 = 0 c) XY: (-3, 3), (-3, 0), (-3, -3) m = (0 - 3) / (-3 - (-3)) = -3 / 0 (cannot divide by 0) d) XY: (-5, -6), (-3, -1), (1, 4) m = (-1 - (-6)) / (-3 - (-5)) = 5 / 2 Write the equation in slope-intercept form (get y by itself). a) 3x + 2y = 6 2y = -3x + 6 y = -3/2x + 3 b) -x - 4y = 8 -4y = x + 8 y = -1/4x - 2 c) y = 6.5 y = 0x + 6.5 d) -2x + y = 4 y = 2x + 4 NOTES Linear Functions REVIEW Name: Date: Period: Row: Find the slope of each line. Slope = rise / run up 3 3 right 5 5 line with a positive slope up 4 4 right 0 0 cannot divide by 0 undefined vertical line 0 0 8 8 0 horizontal line down 2 -2 right 3 3 -2/3 line with a negative slope Find the slope of the line through each pair of points. Change in y divided by change in x (11, -17), (2, -17) (-17 - (-17)) / (2 - 11) = 0 / -9 = 0 (14, 16), (2, 13) (13 - 16) / (2 - 14) = -3 / -12 = 1/4 OR (16 - 13) / (14 - 2) = 3 / 12 = 1/4 (8, 14), (11, 19) (19 - 14) / (11 - 8) = 5/3 (5, 17), (19, -2) (-2 - 17) / (19 - 5) = -19/14 Find the slope of each line. y = mx + b m = slope b = y-intercept y = -7/5x - 2 -7/5 x = -1 undefined y = 3/5x + 1 3/5 y = -9/5x - 4 -9/5 Sketch the graph of each line. Step 1: Start at the y-intercept Step 2: Count the rise (slope) to plot the second point y = -4x - 1 b = -1 m = -4 down 4 right 1 OR up 4 left 1 y = (1/2)x + 3 b = 3 m = 1/2 y = (1/3)x + 0 b = 0 m = 1/3 y = (-3/2)x + 5 b = 5 m = -3/2 4x - 3y = 9 4x - 3y = 9 -4x -4x -3y = -4x + 9 -3y = -4x + 9 -3 -3 y = 4/3x - 3 b = -3 m = 4/3 2x + 5y = 20 2x + 5y = 20 -2x -2x 5y = -2x + 20 5y = -2x + 20 5 5 y = -2/5x + 4 b = 4 m = -2/5