write the equation of the line in point-slope slope-intercept and standard forms where the two points is (5,-6) and (6,-5). 20 points and brainliest to the best answer

Slope-intercept form:   y = x  - 11

Standard form:   y - x = 11

Point-slope form:   y + 5 = (x - 6)

Step-by-step explanation:

Given the two points, (5, -6) and (6, -5):

We must first solve for the slope, as it will be used in the point-slope and slope-intercept forms.  

Let (x₁, y₁) =  (5, -6)

     (x₂, y₂) = (6, -5)

Substitute these values into the following slope formula:

m = 1

Therefore, the slope of the line is 1.

Next, we must determine the y-intercept of the line. The y-intercept is the point on the graph where it crosses the y-axis, at point (0, b). In order to find the y-intercept, use one of the given points, (6, -5), and the slope, m = 1, and substitute into the slope-intercept form, y = mx + b:

y = mx + b

-5 = 1 (6) + b

-5 = 6 + b

Subtract 6 from both sides:

-5 - 6 = 6 - 6 + b

-11 = b

Therefore, the y-intercept is (0, -11), where b = -11.

Now that we have the value for the slope of the line, m = 1, and the y-intercept, b = -11, we could proceed in creating the linear equation in slope-intercept, point-slope, and standard forms.

Given our slope, m = 1, and the y-intercept, b = -11, we can express the linear equation in the following forms:

We could transform the slope-intercept form into the standard form:

Ax + By = C

where:

Transform the slope-intercept form into standard form.

Start by subtracting x from both sides of the equation:

y - x = x  - x - 11

y - x = -11  ⇒  This is the standard form where A = 1, B = -1, and C = -11.

Use one of the given points, (6, -5) and substitute into the point-slope form:

y - y₁ = m(x - x₁)

y - (-5) = 1(x - 6)

y + 5 = (x - 6)   ⇒  This is the point-slope form.

answer: 20

step-by-step explanation:

step-by-step explanation:

let's assume

number of candles set =x

price of of x candles =p(x)

we are given

a candle maker prices one set of scented candles at $10 and sells an average of 200 sets each week

so, we get point as (200,10)

he finds that when he reduces the price by $1, he then sells 50 more candle sets each week

so, we can find slope

now, we can use point slope form of line

now, we can plug values

we can use point

and find b

now, we can plug it back

and we get

now, we can find revenue

we know that

revenue = price*quantity

so, we get