Question 1045367
let x equal the number of minutes.
let y equal the total cost.


total cost for the first plan is y = 5 + .10 * x


total cost for the second plan is y = 8 + .07 * x


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.


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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.


here's a reference.


<a href = "http://www.algebra-class.com/writing-equations-2.html" target = "_blank">http://www.algebra-class.com/writing-equations-2.html</a>


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