# Substitution Equations and Graphing

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Solve the equation

Use substitution to determine whether the ordered pair (-2, 11) is a solution of the equation x2 + y = 15. Show some work. Be sure to state your conclusion about whether the ordered pair is a solution or not.

State the center and the radius of the circle represented by the equation

(x - 9) 2 + (y + 1)2 = 49

(a) Find g(1).

(b) State the domain of the function .

(c) Find g(t + 1) and simplify as much as possible. Show work

Given the piecewise function , determine g(6).

Marie earns a weekly paycheck consisting of base pay of $450, plus a commission of 3.7% of her weekly sales.

(a) Write an equation that can be used to determine Marie's weekly paycheck P, given the amount of weekly sales s.

(b) Determine Marie's weekly paycheck if her weekly sales are $15,420.

A gardener has 80 feet of fencing to make a rectangular garden enclosure. If the enclosure is x feet long, express the area A of the enclosure as a function of the length.

Consider the points (1, -1) and (9, 3).

(a) State the midpoint of the line segment with the given endpoints.

(b) Find the distance between the points. Show some work. Give the exact answer (involving a radical), and also an approximation to three decimal places.

(c) Find the slope of the line passing through the two given points. Show some work.

(a) Find the slope-intercept equation of a line having slope of -2 and containing

the point (5, -3). Show work.

(b) State the slope for a line parallel to the line described in (a).

(c) State the slope for a line perpendicular to the line described in (a).

#### Solution Summary

This provides examples of working with equations to solve, find domain, model problems, and in graphing situations.