Given (1, 5) and (2, 14)
calculate 8 items:
Calculate the slope and point-slope form:
| Slope (m) = | y2 - y1 |
| x2 - x1 |
| Slope (m) = | 14 - 5 |
| 2 - 1 |
| Slope (m) = | 9 |
| 1 |
Slope = 9
Calculate the point-slope form :
y - y1 = m(x - x1)
y - 5 = 9(x - 1)
Calculate the line equation
Standard equation of a line is y = mx + b
where m is our slope
x and y are points on the line
b is a constant.
Rearrange the equation to solve for b
we get b = y - mx.
Use (1, 5) and the slope (m) = 9
b = 5 - (9 * 1)
b = 5 + 9
| b = | -4 |
| 1 |
Solve for b
b = -4
Build standard line equation
y = 9x - 4
Distance between the 2 points
D = Square Root((x2 - x1)2 + (y2 - y1)2)
D = Square Root((2 - 1)2 + (14 - 5)2)
D = Square Root((12 + 92))
D = √(1 + 81)
D = √82
D = 9.0554
Midpoint between the 2 points
| Midpoint = |
| x2 + x1 |
| 2 |
| , |
| y2 + y1 |
| 2 |
| Midpoint = | |
| 1 + 2 |
| 2 |
| , |
| 5 + 14 |
| 2 |
| Midpoint = | |
| 3 |
| 2 |
| , |
| 19 |
| 2 |
Form a right triangle
Plot a 3rd point (2,5)
Our first triangle side = 2 - 1 = 1
Our second triangle side = 14 - 5 = 9
Using the slope we calculated
Tan(Angle1) = 9
Angle1 = Atan(9)
Angle1 = 83.6598°
Since we have a right triangle
We only have 90° left
Angle2 = 90 - 83.6598° = 6.3402
Calculate the y intercept of our line
The y intercept is found by
Setting x = 0 in y = 9x - 4
y = 9(0) - 4
y = -4
Find the parametric equations for the line
Parametric equations are written as
(x,y) = (x0,y0) + t(b,-a)
Plugging in our numbers, we get
(x,y) = (1,5) + t(2 - 1,14 - 5)
(x,y) = (1,5) + t(1,9)
x = 1 + t
y = 5 + 9t
Calculate Symmetric Equations:
| x - x0 | |
| z |
| y - y0 |
| b |
Plugging in our numbers, we get:
| x - 1 | |
| 1 |
| y - 5 |
| 9 |
Plot both points and line on the Cartesian Graph:
Final Answers
Slope Intercept = y = 9x - 4
Distance Between Points = 9.0554
Midpoint = (3/2, 19/2)
Angle 1 = 83.6598
Angle 2 = 6.3402
Y-intercept = -4
