Subjects algebra

Golf Iron Angle 4D4B24

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1. **Problem statement:** We have golf irons numbered 1 to 9 with corresponding angle measures in degrees: 12°, 16°, 20°, 24°, 28°, 32°, 36°, 40°, 44°. We want to find the equation relating the iron number $x$ to the angle $v$. 2. **Identify the pattern:** The angle increases by 4° for each increase of 1 in the iron number. 3. **Write the linear equation form:** Since the relationship is linear, we use the formula for a line: $$v = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 4. **Calculate the slope $m$:** The slope is the change in angle divided by the change in iron number: $$m = \frac{16 - 12}{2 - 1} = \frac{4}{1} = 4$$ 5. **Find the intercept $b$:** Using the point for 1-iron ($x=1$, $v=12$): $$12 = 4 \times 1 + b \implies b = 12 - 4 = 8$$ 6. **Final equation:** $$v = 4x + 8$$ This equation means for any iron number $x$, the angle $v$ can be found by multiplying $x$ by 4 and then adding 8. 7. **Graph description:** Plot points $(1,12), (2,16), (3,20), \ldots, (9,44)$ and draw the line $v=4x+8$ through them. **Answer:** The equation relating iron number $x$ to angle $v$ is $$v = 4x + 8$$.