Question

The two points on the graph are given by the linear function f.
a. Use the two points to find the equation that represents the linear function f.
b. What is​ f(6)?
-1
1
2
3
4
5
-1
1
2
3
x
y



A coordinate system has a horizontal x-axis labeled from negative 1 to 5 in increments of 0.5 and a vertical y-axis labeled from negative 1 to 3 in increments of 0.5. Points are plotted at (1, 2) and (4, 1).
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Part 1
a. The equation ​f(x)equals
  
enter your response here represents the linear function f.
​(Simplify your answer. Type an expression using x as the variable. Use integers or fractions for any numbers in the​ expression.)

Answer 1

a. Slope m = (1 - 2)/(4 - 1) = -1/3. Using point–slope with (1,2): f(x) = -1/3(x - 1) + 2 = -1/3 x + 7/3.

b. f(6) = -1/3(6) + 7/3 = -2 + 7/3 = 1/3.