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Learn how to graph linear equations, find x- and y-intercepts, sketch linear inequalities, and verify points on a line in this informative lesson. Interactive examples provided.

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Do Now

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  1. Do Now • Announcements: • Mandatory office hours to clear missing homework this Saturday.

  2. Students will be able to demonstrate their understanding of verifying points on a line and finding & y-intercepts given an equation or a graph by scoring at least 2 on their exit slip. Objective

  3. Standard 6.0Students graph a linear equation and compute the x- and y-intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4).

  4. The y interceptis the point at which the graph of an equation crosses the y axis. y = 2x + 3 y Notice that the x value is zero. (0,3) x • To find the y-intercept, plug zero (0) in for “x” and solve for y.

  5. The x interceptis the point at which the graph of an equation crosses the x axis. y = 2x + 3 y (-3/2 ,0) x Notice that the y value is zero. • To find the x- intercept, plug zero (0) in for “y” and solve for x.

  6. Ex. Find the x and x intercepts. 1) y = 2x + 6 • 2) 5x – 6y = 8 • 4) 5x + 10y = 40 • 3) 3x + 3y = 6 • 5) 2x + 3y = 6

  7. Verifying Points on a Line Ex 2: Which ordered pair or pairs are solutions of 3x = y + 7? (2, -4) (-2, 3) (1, -2) (2, -1) Ex 1: Which ordered pair or pairs are solutions of 2x -5y = 1 (7, -3) (-2, 1) (-7, -3)(-2, -1)

  8. Verifying Points on a Line Ex 3: Which ordered pairs are solutions of 3x + 3y = 0? (2, -2) (-2, 2) (1, -1) (-1, 1) (2, 2) (1, 1) (5, 5) Ex 4: Which ordered pair or pairs are solutions to 8 -2y = 4x? (0, -2) (2, 0) (1, -2)(-0.5, -3)

  9. Find the x-intercept & y-intercept of the graph below

  10. Find the x-intercept & y-intercept of the graph below

  11. You try Find the x and y intercepts. 1) y = ½ x + 4 2) y = -2 x + 8 4) y = 8x - 2 3) y = -3x - 4 6) 5x + 2y = 10 5) 2x + 3y = 6

  12. Solutions 1) y intercepty = ½ (0) + 4 y = 4(0,4) x intercept0 = ½ x + 4 x = -8(-8,0) 2) y intercepty = -2 (0) + 8 y = 8(0,8) x intercept0 = -2 x + 8 x = 4(4,0) 3) y intercepty = -3 (0) - 4 y = -4(0,-4) x intercept0 = -3 x - 4 x = -4/3(-4/3,0)

  13. Solutions 4) y intercepty = 8 (0) - 2 y = -2(0,-2) x intercept0 = 8 x - 2 x = 1/4(1/4,0) 5) y intercept2(0) + 3y = 6 y = 2(0,2) x intercept2x + 3(0) = 6 x = 3(3,0) 6) y intercept5(0) + 2y = 10 y = 5(0,5) x intercept5x + 2(0) = 10 x = 2(2,0)

  14. Verifying Points on a Line 1) Which ordered pair or pairs are solutions of 2x + 4y = 8? (0, 2) (2, -1) (2, 0) (3, -0.5) 2) Which ordered pair or pairs are solutions of 8x – 4 = 3y? (4, -2) (0, ½) (2, 4) (2/3, -3/4)

  15. Find the x-intercept & y-intercept of the graph below y x

  16. Find the x-intercept & y-intercept of the graph below y x

  17. Exit Slip • Find the x and y intercepts. • -3x + 5y = 9 • -2x - 3y = 10 3) 4)

  18. Exit Slip 5) Which ordered pair or pairs are solutions of 3x + y = 8? (4, -4) (2, 2) (-8, 0) (3, -1) 6) Which ordered pair or pairs are solutions of 3x + 3y = 12? (-3, 1) (-4, 1) (1, 3) (-2, 5)

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