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horsena [70]
3 years ago
10

I need to find the linear function

Mathematics
1 answer:
makkiz [27]3 years ago
4 0

Answer:

y = \frac{1}{2} x + 7

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (2, 8) and (x₂, y₂ ) = (10,12) ← 2 ordered pairs from the table

m = \frac{12-8}{10-2} = \frac{4}{8} = \frac{1}{2}

y = \frac{1}{2} x + c ← is the partial equation

to find c substitute any ordered pair into the partial equation

using (6, 10 ), then

10 = 3 + c ⇒ c = 10 - 3 = 7

y = \frac{1}{2} x + 7 ← linear equation


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