What is the slope of the linear function $f$ $f$ that satisfies: $f (2) = - 3$ $f(2)=-3$ and $f (- 2) = 5$ $f(-2)=5$ ?

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Answer 1 · 2017-03-13T08:29:56

Slope = $- 2$ $-2$

We are told that a linear function $f$ $f$ satisfies:
$f (2) = - 3$ $f(2)=-3$ and $f (- 2) = 5$ $f(-2)=5$

Hence we have a straight line through the points:
$(2, - 3)$ $(2,-3)$ and $(- 2, 5)$ $(-2, 5)$

The equation of a straight line through points $(x_{1}, y_{1})$ $(x_1, y_1)$ and $(x_{2}, y_{2})$ $(x_2, y_2)$ is:

$(y_{2} - y_{1}) = m (x_{2} - x_{1})$ $(y_2 - y_1) = m(x_2-x_1)$ where $m$ $m$ is the slope of the line.

Hence, in our example: $(5 - (- 3)) = m (- 2 - 2)$ $(5-(-3)) = m(-2-2)$

$- 4 m = 8 \to m = - 2$ $-4m=8 -> m=-2$

The equation of a straight line is: $y = m x + c$ $y=mx+c$

Hence, in this case: $- 3 = (- 2) \cdot 2 + c$ $-3=(-2)*2 +c$

$- 3 = - 4 + c \to c = 1$ $-3 =-4+c -> c=1$

The graph of $f$ $f$ is shown below.
graph{-2x+1 [-10, 10, -5, 5]}

What is the slope of the linear function fff that satisfies: f(2)=-3f(2)=−3f(2)=-3 and f(-2)=5f(−2)=5f(-2)=5?