 Complete the tables x5x – 2 -7 -4 0 0 18 -52 xx 2 - 2 -4 0 8 2 -3 9.

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Presentation transcript:

 Complete the tables x5x – xx

9. x – int: (2, 0) y – int: (0, -3) slope: 3/2 y = 3/2x – x – int: (1, 0) y – int: (0, 3) slope: -3 y = -3x x – int: (10, 0) y – int: (0, -2) slope: 1/5 y = 1/5x – x – int: (5, 0) y – int:  slope:  x = 5

 Need help? Look in your book in 2.1  Practice Worksheet

Completing Tables Working Without Graphs Two Variable Word Problems

 To determine the following using algebraic methods: ◦ Equation of a line ◦ Slope of a line ◦ x- and y-intercepts

Point-Slope FormSlope-Intercept Form  y – y 1 = m(x - x 1 )  y – 13 = -2(x + 4)  y – 13 = -2x – 8  y = -2x + 5  y = mx + b  13 = -2(-4) + b  13 = 8 + b  5 = b  y = -2x + 5 m = -2, passing through (-4, 13)

Point – Slope FormSlope – Intercept Form  y – y 1 = m(x - x 1 )  y + 2 = 0(x - 7)  y + 2 = 0  y = -2  y = mx + b  -2 = 0(7) + b  -2 = 0 + b  -2 = b  y = -2 Horizontal line passing through (7, -2)

Point – Slope FormSlope-Intercept Form  y – y 1 = m(x - x 1 )  y - 2 = ½(x - 6)  y - 2 = ½x - 3  y = ½x - 1  y = mx + b  2 = ½(6) + b  2 = 3 + b  -1 = b  y = ½x - 1 Slope: passing through (6, 2) & (10, 4)

Parallel LinesPerpendicular Lines Graph SlopesSame y - interceptDifferent Same (intersect on y – axis) or Different

1. Use first line to determine slope 2. Use point-slope form or slope-intercept form to find equation  Parallel lines have same slope, so m = 4  y + 25 = 4(x + 5)  y + 25 = 4x + 20  y = 4x – 5  -25 = 4(-5) + b  -25 = b  -5 = b  y = 4x - 5 Parallel to y = 4x + 12 & passing through (-5, -25)

1. Use first line to determine slope 2. Use point-slope form or slope-intercept form to find equation  Perp. lines have same slope that are opposite reciprocals, so m = -¼  y - 5 = -¼ (x -12)  y - 5 = - ¼x + 3  y = - ¼x +8  5 = - ¼(12) + b  5 = -3 + b  8 = b  y = - ¼x +8 Perpendicular to y = 4x + 12 & passing through (12, 5)

 Slope: ◦ Rearrange the equation into slope-intercept form ◦ Answer: 2  Y – intercept: ◦ Use slope-intercept form ◦ Or, make x = 0 and solve ◦ Answer: (0, -2)  X – intercept: ◦ Make y = 0 and solve ◦ Answer: (1, 0)

 Slope: ◦ Rearrange the equation into slope-intercept form ◦ Answer: 5/2  Y – intercept: ◦ Use slope-intercept form ◦ Or, make x = 0 and solve ◦ Answer: (0, -10)  X – intercept: ◦ Make y = 0 and solve ◦ Answer: (-2, 0)

 Find the equation of a line without a graph?  Find the slope and intercepts of a line without a graph?