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Andrei [34K]
3 years ago
7

Write the rule for the linear function. Remember a function rule is written using f(x)

Mathematics
1 answer:
Marina CMI [18]3 years ago
4 0

Answer:

The rule for the linear function will be:

f(x) = -2x+5

Step-by-step explanation:

We know that linear function can be represented using the slope-intercept formula

y = mx+b

where m is the slope and b is the y-intercept

Given the function is linear

Taking two points from the table to determine the slope

  • (1, 3)
  • (2, 1)

\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}

\left(x_1,\:y_1\right)=\left(1,\:3\right),\:\left(x_2,\:y_2\right)=\left(2,\:1\right)

m=\frac{1-3}{2-1}

m=-2

Using the point-slope form of the line equation

y-y_1=m\left(x-x_1\right)

where m is the slope of the line and (x₁, y₁) is the point

substituting the values m = -2 and the point (1, 3)

y-y_1=m\left(x-x_1\right)

y - 3 = -2 (x-1)

y-3 = -2x+2

adding 3 to both sides

y-3+3 = -2x+2+3

y = -2x+5

or

f(x) = -2x+5

Therefore, the rule for the linear function will be:

f(x) = -2x+5

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The general form of the desired equation is 
y = mx + b
 where
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