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Wize High School Algebra I Textbook (Common Core) > Linear Functions (Equation of a Line)

Intro to the Equation of a Line

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Equation of a Line

Any linear relation can be represented using a linear equation (a.k.a. equation of a line).

A line is a collection of many points that all follow the same "rule". This rule is called the equation of the line.


Equation of a line

The equation of any straight line looks like y=mx+by=mx+b.
  • Both independent variable (xx) and dependent variable (yy) have degree 1, meaning that they both have a power of 1
  • mm is the slope of the line, and it tells us how steep the line is, also known as the rate of change
  • bb is the y-intercept, and it tells us where the line meets the y-axis (the initial value of the line)
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Example: Equation of a Line

Find 3 different points that are on each of the following lines.

There are many different possible answers!

a)

Three possible answers are (1,−2)(1,-2) , (2,1)(2,1), and (3,4)(3,4).

There are many different possible answers, but it's easier to find points that have "nice" coordinate values -- these are points where the line crosses the grid at a "corner"
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b) y=3x+1y=3x+1

We can find any point on the line by replacing one of the variables with any number and solving for the remaining variable.

Point 1: Let x=0x=0
y=3x+1y=3\colorbox{yellow}{$x$}+1
y=3(0)+1y=3\colorbox{yellow}{$(0)$}+1
y=1y=1
So, one point is (0,1)(0,1).

Point 2 Let x=1x=1
y=3x+1y=3\colorbox{yellow}{$x$}+1
y=3(1)+1y=3\colorbox{yellow}{$(1)$}+1
y=4y=4
So, one point is (1,4)(1,4).

Point 3 Let x=2x=2
y=3x+1y=3\colorbox{yellow}{$x$}+1
y=3(2)+1y=3\colorbox{yellow}{$(2)$}+1
y=7y=7
So, one point is (2,7)(2,7).

Practice: Equation of a Line

Select ALL of the points that are on the line y=2x−5y=2x-5.
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Horizontal & Vertical Lines

Normally, the equation of a line can be written in the form of y=mx+by=mx+b, but how about if we just have a horizontal line or vertical line?

Horizontal Lines (Flat)



Every point on the graph has the same
y
coordinate, so the line is
y = k

Vertical Line (Straight up and down)


Every point on the graph has the same
x
coordinate, so the line is
x = k

Practice: Horizontal and Vertical Lines

Write the equation of each of the following lines.

a)

b)

c)

d)

e)