Lesson 13.2 Equations of Lines

Objective: By the end of this lesson you will be able to write equations of lines given a slope, a point, two points, or any combination. You will also be able to recognize three different forms of equations of

lines.

Mr. Castillo’s Newest Math Metaphor

From the creator of rappers in math prison, I bring you Mr. Castillo’s newest silly math metaphor…

Tales of Lost Math Treasures!

Think first about any treasure movie you have ever seen or read or heard of. Like Goonies, or National Treasure, Indiana Jones, Treasure Island, Pirates of the Caribbean, etc.

Most often, each treasure movie starts the same…someone finds a MAP.

Sometimes the map is given directly to the characters, sometimes the map is ripped up and needs to be reassembled, sometimes the map is booby trapped.

What happens after the characters find the map?

Some will say they go directly after the treasure, but that’s not true.

After finding the map, you must use the map to find the key!

Once you have the key and the map, you may now hunt down the treasure.

Finding math treasure (an equation of a line, y=mx+b) you will need to follow the same procedure.

You first need the map (m or slope).

Sometimes the map will be given to you directly (m=#)

The map may be ripped up in which case you will need to reassemble it.

It may be booby trapped (the slope is perpendicular or parallel to a different equation).

2 1

2 1

y y

x x

Once you have the map (m=#), you will use the map and a starting point to help you find the key (rhymes with “b” from y=mx+”b”)

Once you have the map (m) and the key (b) you will write down the treasure (your answer, which is y=mx+b).

Write the equation of a line containing the points

(-1, 4) and (1, 8).

y = 2x + 6

Some Shortcuts

Horizontal Lines: Horizontal lines have no slope, or in math terms, 0 slope.

So if an equation contained the points (-7, 4) and (3, 4) the equation of the line would be…find the math treasure…

y = 4

The shortcut is, if the two given points share a number (like the y value of the last example) then the equation is simply

y = # shared

Whenever an equation of a line is simply x = #, then the line is a vertical line.

The same shortcut applies to horizontal lines as to vertical lines.

Find the equation of the line that passes through the points (-1, 6) and (-1, 7).

The x values match, so then the equation of the line would be

x = -1

Notice that this time it is not y = shared # since it is not the y values that are matching.

Different forms of a line

Most likely you have only ever learned about y = mx + b (slope-intercept form) in your other

math classes.

There are, however, different forms that are more useful in certain situations in Algebra 2.

We want you to be familiar with these other forms. Here they are.

Point-slope Form

Point-slope Form: Useful if you are given a slope (m) and a single point

1 1( )y y m x x

1 1,x y

General Form

ax + by + c = 0

General Form: a, b, and c are real numbers. General form becomes more useful in higher level math such as calculus and trig.

Examples

Write an equation of a line containing the points (7, -3) and (4, 1).

Find an equation of the line with a slope of 3 and an x-intercept of 5.

Summary

Write down the equations of a horizontal line and a vertical line. What is different about these lines compared to a “slanted” line?

Homework: w/s 13.2