Question

The functions are written in plot slope form state a point on the graph and the slope M

Answer 1

The function given is,

$f(x)=-3+7(x+2)$

We are told to graph the function, state a point (x₀,y₀) and also solve for the slope.

The graph of the function will be shown below

Note:

$-1.571\text{ in fraction is }\frac{\text{-11}}{7}$

From the graph, the points are

$\begin{gathered} (x_1,y_1)\rightarrow(-\frac{11}{7},0) \\ (x_2,y_2)\rightarrow(0,11) \end{gathered}$

The formula for the slope(m) between two points is,

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

Substituting the values of x1 = -11/7, y1 = 0, x2 = 0, y2 = 11 in order to solve for the slope.

$\begin{gathered} m=\frac{11-0}{0--\frac{11}{7}}=\frac{11}{0+\frac{11}{7}}=\frac{11}{\frac{11}{7}} \\ m=11\div\frac{11}{7}=11\times\frac{7}{11}=\frac{77}{11}=7 \\ \therefore m=7 \end{gathered}$

Hence, the slope

$m=7$