Graphing Linear Equations

by

the Slope-Intercept method

The slope-intercept equation of a line is

y = mx + b

m is the slope of the line

b is where the graph crosses the y-axis

The Slope-Intercept Equation

5y – 2x = 15

To use the slope-intercept equation of a line,

y = mx + b

we must first solve for y

Graph using slope-intercept

5y – 2x = 15

Step 1: Get the 2x to the other side of the equal sign

‘Hop and Swap’

If you cross the equal sign, your sign changes!

Hop – 2x across the = and swap its sign!

5y = + 2x + 15

Graph using slope-intercept

5y = + 2x + 15

Step 2: To isolate the y, we must now divide

both sides of the equation by 5

𝑦 =2

5𝑥 + 3

Graph using slope-intercept

𝑦 =2

5𝑥 + 3

In this equation, the slope is 2

5.

The y-intercept is (0, 3)

Notice that we write that as an ordered pair!

Graph using slope-intercept

The first point we are point to graph is the y-intercept

Graph 𝑦 =2

5𝑥 + 3

Remember: slope = riserun

=2

5

Slope tells us how to get from one point to another

on the line.

From one point, if you rise 2 and run 5,

you’ll be back on the line!

The meaning of slope

Graph 𝑦 =2

5𝑥 + 3

A reminder about fractions

2

−5=

− 2

5= −

2

5

These are all equivalent.

A reminder about fractions

−2

5=

2

− 5=

− 2

5

I like to use the rule: Negative signs float.

That way, the top tells you “up” or “down”.

The bottom is “always run right”!

Graphing the equation of a line

1. FIRST solve for y: y = mx + b

2. m is the slope

3. (0, b) is the y-intercept

4. Plot the y-intercept first.

5. Use the slope to ‘walk’ to the next

point.