MA112 – 1.4 Equations of Lines ‘Finding the line from data’
Today:
 1.4: finding the equation for a line
Announcements
 Homework 1.4 due Fri
 Module 1 quiz (today / Fri)
 quiz next class: find equation of the line
through 2 points
A. Line: Simplest Relationship Between x and y
Geometrically, a line can be defined by any 2 distinct points.
Equivalentially, a line can be defined by one point and a direction.
Ingredients for a line:
 a point (place to start)
 a direction (where to go from there)
The ‘direction’ can be provided by another point.
Different Ways of Describing Lines
Slope-Intercept Form
Point-Slope Equation
y  mx  b
m = slope
(0,b) = y-intercept
 direction!
 point!
y  y1  mx  x1 
m = slope
(x1,x2) = arbitrary point
weirder ones: intercept-intercept and parametric
In this section, we will focus on slope-intercept form: y  mx  b .
Finding a line given data
(1) find the slope of the line (find m)
(2) find the y-intercept (find (0,b)) by plugging in any known point
(3) write y  mx  b
Parallel and Perpendicular
 Two lines are parallel if they have the same slope. (If they go through different
points, they are two different lines.)
 Two lines are perpendicular if they have opposite slopes. (Their slopes are negative
reciprocal of one another.)
1
x  7 are perpendicular.
2

y  2 x  10 and y 

find a || or  using the line’s slope and a given point