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

Find the answer for given questions? Slope- intercept? Point slope standard form?-example-1
User Oleksii Balenko
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1 Answer

26 votes
26 votes

Answer:

The equation in slope-intercept form will be;


y=-(1)/(2)x+1

The function in point-slope form is;


y-2=-(1)/(2)(x+2)_{}

The standard form of the equation is;


x+2y=2

Step-by-step 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=(f(8)-f(-2))/(8-(-2))=(-3-2)/(8+2)=(-5)/(10) \\ m=-(1)/(2) \end{gathered}

we can then solve for the constant term;


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

The equation in slope-intercept form will be;


y=-(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=-(1)/(2)(x-(-2)) \\ y-2=-(1)/(2)(x+2)_{} \end{gathered}

The function in point-slope form is;


y-2=-(1)/(2)(x+2)_{}

The standard form of the equation can be written as;


\begin{gathered} y=-(1)/(2)x+1 \\ (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

User Meitham
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