Question

The table shows a linear function.

Which equation represents the function?


f(x)=−53x+9

f(x)=9x+53

f(x)=53x+9

f(x)=−53x−9
x f(x)
−6 −1
−3 4
0 9
3 14

Answer 1

Answer:

$\large\boxed{y=\dfrac{5}{3}x+9}$

Step-by-step explanation:

The slope-intercept form of an equation of a line:

$y=mx+b$

m - slope

b - y-intercept → (0, b)

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

From the table we have an y-intercept (0, 9) → b = 9.

Take other point from the table (-6, -1).

Calculate the slope:

$m=\dfrac{-1-9}{-6-0}=\dfrac{-10}{-6}=\dfrac{5}{3}$

Finally:

$y=\dfrac{5}{3}x+9$