Question

Function of the Day: y+3=-12(x-10)

What do you know?

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Answer 1

1. It’s a linear equation (a straight line).

2. Point-slope form as given: y + 3 = −12(x − 10).

3. Slope-intercept form: y = −12x + 117.

4. Slope m = −12 (rate of change: y decreases 12 units for every +1 in x).

5. It passes through (10, −3) (the point used in the point-slope form).

6. y-intercept: (0, 117).

7. x-intercept: solve 0 = −12x + 117 ⇒ x = 117/12 = 39/4 = 9.75, so (39/4, 0).

8. Standard form: 12x + y = 117.

9. Domain = (−∞, ∞); Range = (−∞, ∞). The line is monotone decreasing (negative slope).

10. Parallel lines have slope −12; a perpendicular line has slope 1/12. (Angle with +x-axis ≈ arctan(−12) ≈ −85.24°.)