Ian and his friends are renting a cabin that charges an initial fee plus a rate per night. The relationship between the cost and number of nights is shown in the graph. What is the cost per night?

writ e an equation to represent this.

Cost per night: 75

Equation:

Step-by-step explanation:

An equation to represent the situation can be written in the slope-intercept form, , where,

m = slope of the graph, which is the rate per night.

b = y-intercept, which is the initial fee. It is the point where the line intercepts the y-axis.

Let's find m, using two points on the line, (2, 200) and (4, 350)

✅The cost per night = 75

y-intercept, b, = 50. The line intercepts the y-axis at y = 50, when x = 0.

Substitute m = 75, and b = 50 into .

✅The equation would be:

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.