Given (3, 22) and (4, 24)
calculate 8 items:
Calculate the slope and point-slope form:
| Slope (m) = | y2 - y1 |
| x2 - x1 |
| Slope (m) = | 24 - 22 |
| 4 - 3 |
| Slope (m) = | 2 |
| 1 |
Slope = 2
Calculate the point-slope form :
y - y1 = m(x - x1)
y - 22 = 2(x - 3)
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 (3, 22) and the slope (m) = 2
b = 22 - (2 * 3)
b = 22 + 6
| b = | 16 |
| 1 |
Solve for b
b = 16
Build standard line equation
y = 2x + 16
Distance between the 2 points
D = Square Root((x2 - x1)2 + (y2 - y1)2)
D = Square Root((4 - 3)2 + (24 - 22)2)
D = Square Root((12 + 22))
D = √(1 + 4)
D = √5
D = 2.2361
Midpoint between the 2 points
| Midpoint = |
| x2 + x1 |
| 2 |
| , |
| y2 + y1 |
| 2 |
| Midpoint = | |
| 3 + 4 |
| 2 |
| , |
| 22 + 24 |
| 2 |
| Midpoint = | |
| 7 |
| 2 |
| , |
| 46 |
| 2 |
Midpoint = (7/2, 23)
Form a right triangle
Plot a 3rd point (4,22)
Our first triangle side = 4 - 3 = 1
Our second triangle side = 24 - 22 = 2
Using the slope we calculated
Tan(Angle1) = 2
Angle1 = Atan(2)
Angle1 = 63.4349°
Since we have a right triangle
We only have 90° left
Angle2 = 90 - 63.4349° = 26.5651
Calculate the y intercept of our line
The y intercept is found by
Setting x = 0 in y = 2x + 16
y = 2(0) + 16
y = 16
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) = (3,22) + t(4 - 3,24 - 22)
(x,y) = (3,22) + t(1,2)
x = 3 + t
y = 22 + 2t
Calculate Symmetric Equations:
| x - x0 | |
| z |
| y - y0 |
| b |
Plugging in our numbers, we get:
| x - 3 | |
| 1 |
| y - 22 |
| 2 |
Plot both points and line on the Cartesian Graph:
Final Answers
Slope Intercept = y = 2x + 16
Distance Between Points = 2.2361
Midpoint = (7/2, 23)
Angle 1 = 63.4349
Angle 2 = 26.5651
Y-intercept = 16
