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Linear Functions Identify and Graph Linear Equations Name and Graph X and Y Intercepts

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Vocabulary for this lesson n Linear Equation – the equation of a line whose graph is a straight line. n Standard Form – Linear equations written in the form Ax + By + C= 0 n X-Intercept – the point where a graphed line crosses the x-axis. n Y-Intercept – the point where a graphed line crosses the y-axis.

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Determine whether each equation is linear….if so, write it in Standard Form nCnCan it be written in standard form? Ax + By = C 1) y = 5 – 2x +2x 2x + y = 5 2) y = -3 – x + x x + y = -3 3) 2xy – 5y = 6 Why?....The first term has TWO variables.

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4) 1 / 3 y = -1 nCnCnCnCan it be written in standard form? Ax + By = C (3) y = -3 5) 5x + 3y = z + 2 Why?....It has an extra variable z. 6) y = x 2 – 8 Why?....Because the x is squared. To be considered LINEAR, an equation must have a degree of ONE.

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x and y - Intercepts To find the x-intercept, let y = 0 To find the y-intercept, let x = 0 The x-int. is 7, so the graph intersects the x-axis at (7, 0) The y-int. is -2, so the graph intersects the y-axis at (0, -2)

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x-intercept (7, 0) y-intercept (0, -2) Now, draw a line through the points.

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Find the x & y intercepts, then graph the equation. 8) x + y = -5 x + 0 = -5 x = -5 (-5, 0) 0 + y = -5 y = -5 (0, -5)

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Find the x & y intercepts, then graph the equation. 9) 3x + 2y = 9 3x + 0 = 9 3x = 9 (3, 0) 0 + 2y = 9 2y = 9 (0, 4.5) x = 3 y = 4.5

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Determine the x & y intercepts of each linear function. 10)xy-3 -201 02 13 11) x-int = -2 Or (-2, 0) y-int = 2 Or (0, 2)

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Real World Examples n x-int. of 20 means that after 20 minutes, the temperature was 0°F. n y-int. of -4 means that at 0 time (the beginning) the temperature was -4°F 12) Determine the x & y intercepts and describe what the intercepts mean.

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Real World Examples 13) Determine the x & y intercepts and describe what they mean. The x-int. doesnt make sense here because it is negative. The y-int. represents the base fare, or cost at zero miles.

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Determine the Intercepts and explain each. 14) Draining a pool 15) Position of a scuba diver. Time (h) Volume (g) 010,080 28640 47200 65760 84320 102880 140 Time (s) Depth (m) 0-24 3-18 6-12 9-6 120 The x-int. shows that after 14 hours, the pool had 0 gallons, or it was completely drained. The y-int. shows that at 0 hours, when they began, it had 10,080 gallons in it. The x-int. shows that after 12 sec., the diver was at the surface (0 m). The y-int. shows that when he started (0 s) he was at -24m or 24m below sea level.

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Exercise

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Challenge

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