Question

Write a linear function f with the values f(-1)=-3 and f(2)=6.

Answer 1

Answer:

y = 3x

Step-by-step explanation:

Equation of a Line

Suppose we know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:

$\displaystyle m=\frac{y_2-y_1}{x_2-x_1}$

The point-slope form of the equation of a line is:

y - k = m ( x - h )

Where m is the slope and (h,k) is a point through which the line passes.

We are given the following values of the function: f(-1)=-3 and f(2)=6. The points are (-1,-3) and (2,6). The slope is:

$\displaystyle m=\frac{6+3}{2+1}=\frac{9}{3}=3$

Now find the equation of the line using the second point:

y - 6 = 3 ( x - 2 )

Operating:

y - 6 = 3x - 6

Simplifying:

y = 3x