# 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 (-4, 5) and (7, -3), we need to calculate 8 items:

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

 Slope (m) = -3 - 5 7 - -4

 Slope (m) = -8 11

Calculate the point-slope form using the formula below:
y - y1 = m(x - x1)
y - 5 = -8/11(x + 4)

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 = (-4, 5) and the slope (m) = -8/11 that we calculated, let's plug in those values and evaluate:
b = 5 - (-8/11 * -4)
b = 5 - (32/11)
 b = 55 11
 -
 32 11
 b = 23 11

This fraction is not reduced. Using our GCF Calculator, we see that the top and bottom of the fraction can be reduced by 23
Our reduced fraction is:
 1 0.22

Now that we have calculated (m) and (b), we have the items we need for our standard line equation:
y = -8/11x + 1/0.22

Item 3: Calculate the distance between the 2 points you entered.
Distance = Square Root((x2 - x1)2 + (y2 - y1)2)
Distance = Square Root((7 - -4)2 + (-3 - 5)2)
Distance = Square Root((112 + -82))
Distance = √(121 + 64)
Distance = √185
Distance = 13.6015

Item 4: Calculate the Midpoint between the 2 points you entered. Midpoint is denoted as follows:
 Midpoint =
 x2 + x1 2
 ,
 y2 + y1 2
 Midpoint =
 -4 + 7 2
 ,
 5 + -3 2

 Midpoint =
 3 2
 ,
 2 2

Midpoint = (3/2, 1)

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 (7,-3)
Our first triangle side = 7 - -4 = 11
Our second triangle side = 5 - -3 = 8

Using the slope we calculated, Tan(Angle1) = -0.73
Angle1 = Atan(-0.73)
Angle1 = -36.0274°
Since we have a right triangle, we only have 90 degrees left, so Angle2 = 90 - -36.0274° = 126.0274

Item 6: Calculate the y intercept of our line equation
The y intercept is found by setting x = 0 in the line equation y = -8/11x + 1/0.22
y = -8/11(0) + 1/0.22
y = 1/0.22

Item 7: Determine the parametric equations for the line determined by (-4, 5) and (7, -3)
Parametric equations are written in the form (x,y) = (x0,y0) + t(b,-a)
Plugging in our numbers, we get
(x,y) = (-4,5) + t(7 - -4,-3 - 5)
(x,y) = (-4,5) + t(11,-8)
x = -4 + 11t
y = 5 - 8t

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

Plugging in our numbers, we get:
 x - -4 11
 y - 5 -8

ANSWERS:
<-- Slope
<-- Slope Intercept Form Line Equation
<-- Distance between points
<-- Midpoint
<-- Angle 1
<-- Angle 2
<-- Y intercept