using point 1, P1 (6,4) and slope m =4/3 or 1.33 in decimal substitutes these values in Equation 1 shown below

Formula memory recall:
y = mx + b
in slope form --equation 1

important to remember variable letter b is your y - intercept value.

Using Point 1 (6,4) : y1 = 4 substitute y = 4 in equation 1 ; then x1 = 6 and finally m=1.33
Why ? In order to get the original value of b, the y-intercept that will connect at point 1 coordinate (6,4) to create the given slope m=4/3 or 1.3333

After you input the value of y1, x1 , and slope, m . It should look like shown below.

y₁ = m *

x₁ + b


Using the above equation you can solve for the value of b, the y-intercept.

For scenario analysis, just change any value in white input box. Then input new value of x2 to compute the answer.

For example new P1(4,2.33) and slope m = 1.333. Solve for the value of y2 given P2(0, y2). Here x2 = 0
this line is parallel to given line but at higher value or designated maximum value.

Maximum line y = 1.3333x - 3

Given line y = 1.3333x - 4

Minimum line y = 1.3333x - 5



For example new P1(4,0.3336) and slope m = 1.333. Solve for the value of y2 given P2(0, y2). Here x2 = 0
this line is parallel to given line but at lower value or designated minimum value.

Special case: For example new P1(7,5) and new slope m = 4. Solve for the value of y2 given P2(1, y2). Here x2 = 1

b = is the answer for variable "b" after doing algebraic calculation from above equation 1.

To find the distance between two points, you need to memory recall your acquired knowledge about Pythagorean equation formula and relate it to slope formula and right triangle formula. Finally c² = a² + b²
a ² = ( X₂ - X₁ )²
b ² = ( Y₂ - Y₁ )²
distance, c = √a ² + b ²

Discovered line equation
y = x + written in slope form.

using point,P2 ( y₂) substitutes its values in discovered equation of a line.

TO SOLVE you must enter new value of x2 = 1 for new scenario example.

y₂ = * + written in slope form.

Remember when the slope of two or three lines are the same they are parallel to each other (remember the letter symbol " m " for slope ). This could happen for example Line maximum (y=1.3333x -3) , Line average (y=1.3333x -4) , and Line minimum (y=1.3333x -5) see line graph above. This knowledge is important in machine learning and statistical analysis where you set the upper limit or maximum confidence level and the lower limit or minimum confidence level.

y₂ = answer

Solving for distance, c

Given
P1 ( x₁ , y₁ )

Given
P2 ( x₂ , y₂ )

Distance, c = answer