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Find a liner equation f(x) with slope 5 such that f(3)=12

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Chris F. | Electronics Engineer with great math skillsElectronics Engineer with great math ski...
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Using f(x) the formula would be f(x) = 5x + b. The standard form of the slope intercept formula is
y = mx + b. The slope is represented by m, which equal 5. Since you know that f(3) = 12, the only unknown is b. So you simply plug in the known information and solve.
  y = mx + b
12 = 5(3) + b
12 = 15 + b
Subtract 15 from both sides.
b = -3
Prove the formula.
12 = 5(3) - 3
12 = 15 - 3
12 = 12
 
Uzair Q. | Perfect 5-star rating in over 100 subjectsPerfect 5-star rating in over 100 subjec...
5.0 5.0 (150 lesson ratings) (150)
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1. y = mx + b
 
2. (12) = (5)(3) + b
 
3. 12 = 15 + b
 
4. 12 - 15 = 15 + b - 15
 
5. -3 = b
 
y = 5x - 3
Susan L. | Tutor in Math and Science--Patient, Proficient, OrganizedTutor in Math and Science--Patient, Prof...
5.0 5.0 (11 lesson ratings) (11)
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The slope intercept form of a straight line equation is
 
y = m x + b
 
where m = slope, b = y-intercept and y = f(x)
 
Plug in what is given to solve for unknown.
 
given x=3, f(3) = 12 = y, m=5
 
12 =  5(3) + b
solve for b
b = 12 - 15 = -3
 
The resulting linear equation using slope = 5 and b = -3 is
 
y = 5x - 3