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.