AlgebraHardFinding the slope from a point
Algebra practice question
In the xy-plane, the graph of the linear function f(x) = mx + 8, where m is a constant, passes through the point (4, 28).
What is the value of m?
- A. 5Correct
- B. 7
- C. 9
- D. 20
Answer: A. 5
Substitute the point into the function: 28 = m(4) + 8. Subtract 8 from both sides: 20 = 4m. Divide by 4: m = 5. (Check: 5(4) + 8 = 28.)
Why the other answers are wrong
- B. 7
- You divided the y-value by the x-value, 28 / 4 = 7, which ignores the constant 8. Subtract the 8 before dividing.
- C. 9
- You added 8 instead of subtracting it: (28 + 8) / 4 = 9. The 8 is already included in the 28, so it must come off.
- D. 20
- 20 is 28 - 8, the part of the output produced by mx. You still need to divide by x = 4 to isolate m.
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