Every Fact About Lines and Linear Equations in One Song Lyrics

Oh there's lines, forms of lines

All these equations in disguise

Yeah lines, forms of lines

You just can't let them fool your mind

Oh we've got standard form

a x plus b y equals c

Slope intercept form

y equals m x plus b

Point slope form

y minus y one equals m times x minus x one

Oh there's lines, lots of lines

You just need two points to form a line

Yeah lines, lots of lines

Or a point and slope is fine

Yeah, we've got horizontal lines

Whose equation is just y equals a number

Vertical lines

Whose equation is just x equals a number

Rising lines have a slope that's positive

Falling lines have a slope that's negative

Parallel lines have exact same slopes

They're also called inconsistent lines

They'll never ever ever ever intersect

The lines with the same slope and y intercept

Are dependent lines, they coincide

Perpendicular lines have negative reciprocal slopes

And cross once in the x y plane

And now that you mention the x y plane

The x axis is a horizontal line

Doesn't have a slope, so y equals zero

The y axis is a vertical line, x equals zero

Slope is undefined

Lines with different slopes only cross one time

Where they intersect is called a solution

To solve a system of linear equations

Use elimination or substitution

If you happen to see an inequality sign

Either draw a dotted or solid line

It depends if there's a line right under the sign

Then shade the region where the solution is defined

The slope of a line is just rise over run

The change in y over change in x

And if you're still perplexed, just study those lines

And that's it folks, see you next time