Question

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

What do you know?

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Vocabulary Terms - Define/Illustrate

Initial value
X - intercept
Domain/Range

Answer 1

Function: y + 3 = -12(x − 10)

What I know:

1. The equation is in point‑slope form: y − (−3) = −12(x − 10). The point used is (10, −3).
2. Slope (m) = −12.
3. Slope‑intercept form: y = −12x + 117.
4. The line is decreasing (because slope is negative) and is very steep (|slope| = 12).
5. y‑intercept (initial value) = 117, point (0, 117).
6. x‑intercept: set y = 0 → 0 = −12x + 117 → x = 117/12 = 39/4 = 9.75, point (39/4, 0).
7. The line passes through (10, −3) (check: substituting x = 10 gives y = −3).
8. Standard form: 12x + y = 117 (or 12x + y − 117 = 0).
9. Any line parallel to this has slope −12; any line perpendicular has slope 1/12.
10. Domain = (−∞, ∞); Range = (−∞, ∞) (since this is a nonhorizontal linear function).

Vocabulary — Define and illustrate with this function:

- Initial value: In function contexts, the initial value is the output when x = 0 (the y‑intercept). For this function the initial value = 117 (point (0,117)).

- X‑intercept: The x value where the graph crosses the x‑axis (y = 0). For this function x‑intercept = 39/4 = 9.75, so the x‑intercept point is (39/4, 0).

- Domain/Range: Domain = all allowable input x values; Range = all possible output y values. For any nonvertical linear function, Domain = (−∞, ∞) and Range = (−∞, ∞). For this line specifically Domain = (−∞, ∞), Range = (−∞, ∞).