Question

Write a linear function f with the values f(-4)=0 and f(4)=2

Answer 1

`\text{Answer : y = }(1)/(4)x\text{ + 1}`

Let f(x) = y

When x = -4 , y = 0

when x = 4 , y = 2

`\begin{gathered} x1\text{ = -4 -4, y1 = 0, x2 = 4, y2 = 2} \\ Firstly,\text{ find the slope} \\ \text{Slope = }\frac{rise}{\text{run}} \\ \text{Slope = }\frac{y2\text{ - y1}}{x2\text{ - x1}} \\ \text{Slope = }\frac{2\text{ - 0}}{4\text{ - (-4)}} \\ \text{Slope = }\frac{2}{4\text{ + 4}} \\ \text{Slope= }(2)/(8) \\ \text{Slope = }(1)/(4) \\ \text{The equation of a linear function} \\ y\text{ = mx + b} \\ (y\text{ - y1) = m(x -x1) } \\ (y\text{ - 0) = }(1)/(4)(x\text{ -(-4)} \\ y\text{ - 0 = }(1)/(4)(x\text{ + 4)} \\ y\text{ - 0 = }(1)/(4)x\text{ + }\frac{1\text{ x 4}}{4} \\ y\text{ - 0= }(1)/(4)x\text{ + 1} \\ y\text{ = }(1)/(4)x\text{ + 1} \\ \text{The linear function is y = }(1)/(4)x\text{ + 1} \end{gathered}`