Linear Equations in Point-Slope Form

Example 1

Earlier, you were told that the cost of a wedding was a function of the number of guests attending. If you knew the slope of the function and you also knew how much the wedding would cost if 150 guests attended, could you write a linear equation representing this situation? If so, what form of the equation would be easiest to use?

Yes, you could write a linear equation if you knew the slope of the function and how much the wedding would cost if 150 guests attended. The price of the wedding if 150 guests attended would be one point on the line. Then, you could use point-slope form to write an equation. Point-slope form would be the best because those are the pieces of information that you have. If absolutely necessary, you could transform the equation into a function in slope-intercept form. 

Example 2

Rewrite \(\begin{align*}y-5=3(x-2)\end{align*}\) in slope-intercept form.

Use the Distributive Property to simplify the right side of the equation:

\(\begin{align*}y-5=3x-6\end{align*}\)

Solve for \(\begin{align*}y\end{align*}\):

\(\begin{align*}y-5+5& =3x-6+5\\ y& =3x-1\end{align*}\)