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Linear Functions

Linear Functions. Identify and Graph Linear Equations Name and Graph X and Y Intercepts. Vocabulary for this lesson. Linear Equation – the equation of a line whose graph is a straight line. Standard Form – Linear equations written in the form Ax + By = C

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Linear Functions

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

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

  3. Can it be written in standard form? Ax + By = C Determine whether each equation is linear….if so, write it in Standard Form 1) y = 5 – 2x Yes +2x +2x 2x + y = 5 2) y = -3 – x Yes + x + x x + y = -3 3) 2xy – 5y = 6 No Why?....The first term has TWO variables.

  4. (3) (3) 4) 1/3 y = -1 Yes y = -3 • Can it be written in standard form? Ax + By = C No 5) 5x + 3y = z + 2 Why?....It has an extra variable “z”. No 6) y = x2 – 8 Why?....Because the “x” is squared. Another way to look at this..... To be considered LINEAR, an equation must have a degree of ONE.

  5. 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)

  6. You can also graph using the intercepts. x-intercept (7, 0) y-intercept (0, -2) Now, draw a line through the points.

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

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

  9. Determine the x & y intercepts of each linear function. 10) 11) y-int. = 3 or (0, 3) x-int. = -4 or (-4, 0) x-int = -2 Or (-2, 0) y-int = 2 Or (0, 2)

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

  11. Determine the x & y intercepts and describe what they mean. Real World Examples x-int. = -3 or (-3, 0) y-int. = 2.25 or (0, 2.25) The x-int. doesn’t make sense here because it is negative. The y-int. represents the base fare, or cost at zero miles.

  12. 14) Draining a pool 15) Position of a scuba diver. Determine the Intercepts and explain each. 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. 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.

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