Question

Find the answer for given questions? Slope- intercept? Point slope standard form?

Answer 1

Answer:

The equation in slope-intercept form will be;

$y=-\frac{1}{2}x+1$

The function in point-slope form is;

$y-2=-\frac{1}{2}(x+2)_{}$

The standard form of the equation is;

$x+2y=2$

Explanation:

Given the function f(x);

$\begin{gathered} f(-2)=2 \\ f(8)=-3 \end{gathered}$

Firstly, let us find the slope;

$\begin{gathered} m=\frac{f(8)-f(-2)}{8-(-2)}=\frac{-3-2}{8+2}=\frac{-5}{10} \\ m=-\frac{1}{2} \end{gathered}$

we can then solve for the constant term;

$\begin{gathered} y=mx+b \\ at\text{ f(-2)=2;} \\ 2=-\frac{1}{2}(-2)+b \\ 2=1+b \\ b=2-1 \\ b=1 \end{gathered}$

The equation in slope-intercept form will be;

$y=-\frac{1}{2}x+1$

Applying the point-slope form of equation;

$y-y_2=m(x-x_2)$

Substituting the second point;

$\begin{gathered} y-2=-\frac{1}{2}(x-(-2)) \\ y-2=-\frac{1}{2}(x+2)_{} \end{gathered}$

The function in point-slope form is;

$y-2=-\frac{1}{2}(x+2)_{}$

The standard form of the equation can be written as;

$\begin{gathered} y=-\frac{1}{2}x+1 \\ \frac{1}{2}x+y=1 \\ \text{multiply through by 2} \\ x+2y=2 \end{gathered}$

The standard form of the equation is;

$x+2y=2$