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Slope-Intercept Form of a Linear EquationAlgebra

y = mx + b

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Graphing a Line

Review: In order to graph the equation of a line, we need an equation.

X Y (x, y)

-1

0

1

We also need a table with some values for “x”.

Y= 3x - 1

Finally, we need to do the math to complete the table and eventually graph the line.

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Our completed table would look like this.

X Y (x, y)

-1 -4 (-1,-4)

0 -1 (0, -1)

1 2 (1, 2)

When we graph the points and connect each one with a single line, the graph looks like this.

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Let’s take some time and examine this graph a little more closely.

We will begin by determining the slope from the graph.To move from one point to another we must travel up 3 and right 1. As a fraction this is 3/1.

3

1

Y=3x -1

Compare the equation with the slope of the line, do you notice any similarities?

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Finally, take a look at the point where the line crosses the y-axis. What is the y-coordinate?

Y=3x -1

(0, -1)

Do you see any similarities between the equation and the y-coordinate?

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The equation you were originally given was written in a special form called:

SLOPE-INTERCEPT FORM.

Y = mx + b

The variable “y” stands for

the y-coordinate

in your ordered pair.

The variable “m” stands

for the slope of the line

which gives directions from one point to

another on the graph

The variable “x” stands for

the x-coordinate

in your ordered pair.

The variable “b” stands

for the y-coordinate

of the y-intercept for the graph of the line (this is used as a

starting point).

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Getting to know the formula

Start by identifying the parts of the equation using the formula: y = mx + b.In our given equation, we can now identify the slope of our line! REMEMBER that slope tell us how the line moves around the graph (like a GPS system).

EXAMPLE: y = 2/3x + 1

In this example our slope is identified as 2/3. ** This means that to move from one point to another on the line, we rise up 2 and run over 3.

In our given equation, we can now also identify they-intercept which is a point on the graph! This will be used a our starting point for our line. REMEMBER that the y-intercept is written as a point (0, y).

In this example b=1, therefore our y-intercept is the point on the graph located at (0, 1)**The point is located on the vertical, y-axis.

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Graphing the Line

EXAMPLE: y = 2/3x + 1 Start by plotting your

y-intercept on the graph. Remember this was (0, 1)

From this point we use our slope to find the next two points on the graph. Remember the top number refers to the rise and the bottom refers to the run.

€

2 ↑

3→

€

↓2← 3

Finally, we connect the points with a straight line.

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Let’s Try Another!

EXAMPLE: y = -2/5x - 3 Start by plotting your

y-intercept on the graph. Remember this was (0, -3)

From this point we use our slope to find the next two points on the graph. Remember the top number refers to the rise and the bottom refers to the run.

€

↑2← 5

€

↓2→5

Finally, we connect the points with a straight line.

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Your turn!

Problem: y = 1/3x+ 4

m = 1/3 OR -1/-3

Y-intercept (0,4)

Connect the points