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.

10000

step-by-step explanation: divide by 2,