Post on 12-Jan-2016
Writing linear equations given two points
5.312/5/13
The slope of a line…
• Mathematicians have developed a useful measure of the steepness of a line, called the slope of the line. Slope compares the vertical change (the rise) to the horizontal change (the run) when moving from one fixed point to another along the line. A ratio comparing the change in y (the rise) with the change in x (the run) is used calculate the slope of a line.
The Slope of a Line
Definition of Slope
The slope of the line through the distinct points (x1, y1) and (x2, y2) is
where x1 – x2 = 0.
Definition of Slope
The slope of the line through the distinct points (x1, y1) and (x2, y2) is
where x1 – x2 = 0.
Change in y
Change in x=
Rise
Run=y2 – y1
x2 – x1
(x1, y1)
x1
y1
x2
y2
(x2, y2)Risey2 – y1
Runx2 – x1
x
y
The Possibilities for a Line’s Slope
Positive Slope
x
y
m > 0
Line rises from left to right.
Zero Slope
x
y
m = 0
Line is horizontal.
m is undefined
Undefined Slope
x
y
Line is vertical.
Negative Slope
x
y
m < 0
Line falls from left to right.
Finding Slope…
• We can find slope 2 ways
1 - Graphing
2 - Slope equations
Finding Slope...
• Find the slope of the line through the points (4, 1) and (-1, 5)
Finding Slope...
• Find the slope of the line through the points (0 , -1) and (5, 9)
Finding Slope..
• Find the slope of the line through the points (3 , 4) and (3 , 9)
Sample Problems:
• Find the slope of the line thru the points given: (-3,-1) and (-2,4)
(-3,4) and (2,-2)
m 4 1 2 3
5
15
m 2 4
2 3 6
5
So…Writing Equations Now…
• When Given 2 points, first find the slope.
• Once you find the slope, you have a slope and a point (2 points actually!)
• Plug in the slope and a point to find the equation
Hold up…
• If we have two points, does it matter which one we choose?
• No…Since both points are on the line, doesn’t matter which one we choose.
Writing Equations
• Find the equation of the line passing through the points:
(0 , -1) and (5 , 9)
Writing Equations
• Find the equation of the line passing through the points:
(1 , 6) and (3 , -4)
Writing Equations
• Find the equation of the line passing through the points:
(6 , -3) and (0 , 9)
Writing Equations
• Find the equation of the line passing through the points:
(4 , -6) and (4 , 4)
Homework:
• On your handout…
Place your name, date, and hour on the worksheet
Write all answers and show all work!!!
Worksheet due Tuesday, 12/10/13