Question

Write the linear function for the given function values.
f(-2)=9 and f(6)=7

Answer 1

`y = -\frac14x + 8.5`

Explanation:

Hello!

A linear function is written in the form of
`y = mx + b`, where m is the slope and b is the y-intercept.

Each of these expressions can be converted to coordinate form, (-2,9) and (6,7).

Slope

Slope can be calculated by the difference in the x-values divided by the difference in the y-values.

Solve

• 
  `(9 - 6)/(-2 - 6)`
• 
  `(2)/(-8)`
• 
  `-\frac14`

The slope is -1/4.

Y-intercept

The y-intercept is found by plugging in the x and y values of a coordinate and the slope and then solving for b.

Solve

• 
  `y = mx + b`
• 
  `9 = -\frac14(-2) + b`
• 
  `9 = 0.5 + b`
• 
  `8.5 = b`

Equation

We can find the equation by simply plugging in all the values that we found.

Equation:
`y = -\frac14x + 8.5`