In Linear Equations, Formulas, and Applications, you will learn the three ways to represent the equation of a line: general equation, slope-intercept form, and point-slope form. Then, we will work on graphing. We will learn that it only takes two points to determine the graph of a line. We can obtain these points from the x-intercept and the y-intercept. Last, we discuss formulas and applications. As far as applications are concerned one that arises deals with comparing the total costs between purchasing services from two competing companies. Hope all of you enjoy the supplement as well as the practice problems!
The supplement for this section from Intermediate Algebra can be accessed here.
Next, I will give some practice problems. I will provide the solutions to these later.
1) What is the equation of the line that passes through the points (-4, -6) and (2, 5)?
2) What are the slope, x-intercept, and y-intercept of the line y = 6x + 7?
3) If f(x) = -x - 7 and g(x) = 6x + 4, then what are f(g(x)) and g(f(x))?
4) Acme Phone Company charges $0.10 a phone call at $0.02 per minute. Excellence Phone Company charges $0.05 a phone call at $0.04 per minute.
(a) Write an equation for the cost of making a phone call with Acme Phone Company. Write an equation for the cost of making a phone call with Excellence Phone Company.
(b) Use the equations to find the point where the two lines intersect. What is the point of intersection?
(c) Graph both of the equations on the same set of axes. Label your axes, include the point of intersection from (b) and label the graphs of both of the equations. Clearly show which one belongs to Acme Phone Company or Excellence Phone Company.
(d) When is Acme Phone Company more expensive than Excellence Phone Company?
(e) When is Excellence Phone Company more expensive than Acme Phone Company?
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