SOLUTION: A telephone company offers customers two payment plans for monthly service. Plan A costs $5 per month plus $0.10 per minute for calls. Plan B cost $8 per month plus $0.07 minute fo
Algebra ->
Test
-> SOLUTION: A telephone company offers customers two payment plans for monthly service. Plan A costs $5 per month plus $0.10 per minute for calls. Plan B cost $8 per month plus $0.07 minute fo
Log On
Question 1045367: A telephone company offers customers two payment plans for monthly service. Plan A costs $5 per month plus $0.10 per minute for calls. Plan B cost $8 per month plus $0.07 minute for calls. 1. Write an equation for each plan. Are these equations in standard form or Slope-intercept form? Answer by Theo(13342) (Show Source):
these equations are in slope intercept form after you re-order the terms in descending order of degree, which is y = mx + b.
reorder the terms of each equation and you get:
y = .10 * x + 5
y = .07 * x + 8
that's slope intercept form.
m is the slope and b is the y-intercept.
in the first equation, the slope is .10 and the y-intercept is 5.
in the second equation, the slope is .07 and he y-intercept is 8.
the y-intercept is the value of y when x = 0.
the slope is the change in the value of y divided by the change in the value of x.
the formula for that is m = (y2-y1) / (x2-x1).
(x1,y1) and (x2,y2) are any two different points on the line of each equation.
your graph will look like this.
the blue line is y = .07x + 8.
the red line is y = .10x + 5.
from the graph, you can see that the plans break even when x = 100 and y = 15.
y = 5 + .10 * x becomes y = 5 + .10 * 100 becomes y = 5 + 10 becomes y = 15.
y = 8 + .07 * x becomes y = 8 + .07 * 100 becomes y = 8 + 7 becomes y = 15.
slope intercept form is y = mx + b
m is the slope and b is the y-intercept.
standard form is ax + by = c
a is the coefficient of the x term.
b is the coefficient of the y term.
c is the constant term.
a must be positive.
a,b, and c must be integers.
that's the strict definition.
conversion from slope intercept form to standard form would proceed as follows for the equation of y = 5 + .10 * x
subtract .10 * x from both sides of the equation to get:
-.10 * x + y = 5
multiply both sides of the equation by -1 to get:
.10 * x - y = -5
multiply both sides of the equation by 10 to get:
x - 10y = -50
by convention, the standard form of the equation has a positive coefficient for the x term and the coefficients of the x term and the y term and the constant term are integers.
your other equation would be converted to standard equation as follows:
start with y = .07 * x + 8
subtract .07 * x from both sides of the equation to get:
-.07 * x + y = 8
multiply both sides of the equation by -100 to get:
7x - 100y = -800
your 2 equations in standard form are:
x - 10y = -50
7x - 100y = -800
you convert these to slope intercept form by solving for y and then re-ordering the terms in descending order of degree.
start with x - 10y = -50
subtract x from both sides of the equation to get -10y = -x - 50
divide both sides of the equation by -10 to get y = -1/-10 * x - 50/-10
simplify to get y = .10 * x + 5.
start with 7x - 100y = -800
subtract 7x from both sides of the equation to get -100y = -7x - 800
divide both sides of the equation by -100 to get y = -7/-100 * x -800/-100
simplify to get y = .07x + 8
