Line Equation-Slope-Distance-Midpoint-Y intercept Calculator

Enter 2 points below or 1 point and the slope of the line equation and press the appropriate button

Point 1: (x1 = , y1 = ) Slope:

Point 2: (x2 = , y2 = ) b:

Given the two points you entered of (1, 4) and (5, 6), we need to calculate 8 items:

Item 1: Calculate the slope and point-slope form:
 Slope (m) = y2 - y1 x2 - x1

 Slope (m) = 6 - 4 5 - 1

 Slope (m) = 2 4

Since the slope is not fully reduced, we reduce numerator and denominator by the (GCF) of 2
Slope = (2/2)/(4/2)
Slope = 1/2

Calculate the point-slope form using the formula below:
y - y1 = m(x - x1)
y - 4 = 1/2(x - 1)

Item 2: Calculate the line equation that both points lie on.
The standard equation of a line is y = mx + b where m is our slope, x and y are points on the line, and b is a constant.

Rearranging that equation to solve for b, we get b = y - mx. Using the first point that you entered = (1, 4) and the slope (m) = 1/2 that we calculated, let's plug in those values and evaluate:
b = 4 - (1/2 * 1)
b = 4 - (1/2)
 b = 8 2
 -
 1 2
 b = 7 2

This fraction is not reduced. Using our GCF Calculator, we see that the top and bottom of the fraction can be reduced by 7
Our reduced fraction is:
 1 0.29

Now that we have calculated (m) and (b), we have the items we need for our standard line equation:
y = 1/2x + 1/0.29

Item 3: Calculate the distance between the 2 points you entered.
Distance = Square Root((x2 - x1)2 + (y2 - y1)2)
Distance = Square Root((5 - 1)2 + (6 - 4)2)
Distance = Square Root((42 + 22))
Distance = √(16 + 4)
Distance = √20
Distance = 4.4721

Item 4: Calculate the Midpoint between the 2 points you entered. Midpoint is denoted as follows:
 Midpoint =
 x2 + x1 2
 ,
 y2 + y1 2
 Midpoint =
 1 + 5 2
 ,
 4 + 6 2

 Midpoint =
 6 2
 ,
 10 2

Midpoint = (3, 5)

Item 5: Form a right triangle and calculate the 2 remaining angles using our 2 points:
Using our 2 points, we form a right triangle by plotting a 3rd point (5,4)
Our first triangle side = 5 - 1 = 4
Our second triangle side = 6 - 4 = 2

Using the slope we calculated, Tan(Angle1) = 0.5
Angle1 = Atan(0.5)
Angle1 = 26.5651°
Since we have a right triangle, we only have 90 degrees left, so Angle2 = 90 - 26.5651° = 63.4349

Item 6: Calculate the y intercept of our line equation
The y intercept is found by setting x = 0 in the line equation y = 1/2x + 1/0.29
y = 1/2(0) + 1/0.29
y = 1/0.29

Item 7: Determine the parametric equations for the line determined by (1, 4) and (5, 6)
Parametric equations are written in the form (x,y) = (x0,y0) + t(b,-a)
Plugging in our numbers, we get
(x,y) = (1,4) + t(5 - 1,6 - 4)
(x,y) = (1,4) + t(4,2)
x = 1 + 4t
y = 4 + 2t

Calculate Symmetric Equations:
 x - x0 z
 y - y0 b

Plugging in our numbers, we get:
 x - 1 4
 y - 4 2