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Slope and y-Intercept Form

This chapter explores the essential concepts of slope and y-intercept in coordinate geometry. It defines intercepts as points where graphs intersect the axes, specifically x-intercepts (where y=0) and y-intercepts (where x=0). Using the slope-intercept form of equations, y=mx+b, we illustrate how to derive slopes and y-intercepts from linear equations. Additionally, we discuss how to write equations of lines given slopes and intercepts, and how to find y-intercepts for lines passing through specific points. Practice questions at the end reinforce understanding.

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Slope and y-Intercept Form

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  1. Chapter 6 Coordinate Geometry 6.6 Slope and y-Intercept Form 6.6.1 MATHPOWERTM 10, WESTERN EDITION

  2. Intercepts An intercept is the point where the graph intersects the axis. The x-intercept is the point where the graph intersects the x-axis. This is the point wherey = 0. The y-intercept is the point where the graph intersects the y-axis. This is the point where x = 0. The y-intercept is 4. It is the point (0, 4). The x-intercept is 5. It is the point (5, 0). 6.6.2

  3. The Slope and y-Intercept Form 1 Graph y = 2x + 3: 2 1 x y 2 -1 1 Increase of 2 1 Increase of 1 0 3 Increase of 2 Increase of 1 2 1 5 Increase of 1 Increase of 2 2 7 As y increases by 2, x increases by 1. This is a rise of 2 for a run of 1. The slope of this line is or 2. The y-intercept is the y value when x = 0. Therefore, the y-intercept is 3. NOTE: In the equation y = 2x + 3, the coefficient of the x-term is 2(the slope) and the constant is 3 (the y-intercept). 6.6.3

  4. The Slope and y-Intercept Form Equations written in the form y = 2x + 3 tell us the slope and y-intercept. The slope and y-intercept form of the equation is: y =mx+ b m = slope b = y-intercept State the slope and y-intercept of the following equations. 3x + 5y - 10 = 0 5y = -3x + 10 slope = y-intercept = 6 slope = y-intercept = 2 6.6.4

  5. Writing the Equation of a Line Given the Slope and a Point Given the slope and y-intercept, find the equation of the line in slope and y-intercept form andin standard form. m = m = b = - 5 b = -2 y = mx + b y = x - 5 y = x -2 3y = -2x - 15 2x + 3y + 15 = 0 5y = 4x - 10 0 = 4x - 5y - 10 4x - 5y -10 = 0 standard form standard form 6.6.5

  6. Writing the Equation of a Line From Its Graph (0, 5) (0, 3) (2, 1) (-2, 0) y-intercept = 5 y = x + 5 2y = 5x + 10 0 = 5x - 2y + 10 5x - 2y + 10 = 0 y = -1x + 3 x + y - 3 = 0 6.6.6

  7. Finding the y-Intercept Given y = 2x + b, find the value of b if the line passes through the following points: (9, 2) (6, 18) y = 2x + b 2 = 2(9) + b 2 = 18 + b -16 = b y = 2x + b 18 = 2(6) + b 18 = 12 + b 6 = b 6.6.7

  8. Assignment Suggested Questions: Pages 288 and 289 1 - 35 odd, 37ac, 38ac, 42, 45, 48 6.6.8

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