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