Graphing using Slope-intercept method.
First, put the equation in Slope-intercept form: y = mx +b (solve for y)
 The ‘b’ is the y-intercept; it is plotted on the y-axis. (0, 𝑏)
 The ‘m’ is the slope: is it the coefficient (number) and SIGN with ‘x’.
o
The slope is plotted starting from the y-intercept….NOT the origin
To Graph the line ***make sure the equation is in slope-intercept form***
𝒚 = 𝒎𝒙 + 𝒃
1. Plot ‘b’ first; ALWAYS start at the origin.
 If ‘b’ is positive, start at the origin, and go that many units up. Make
a point and STOP.
 If ‘b’ is negative, start at the origin, and go that many units down.
Make a point and STOP.
 If there is no ‘b’, then the value of ‘b’ is zero. Make a point at the
origin and STOP.
2. Handle the slope (m) next. WHEN you plot the slope (m), start from
the point you plotted for your y-intercept (b) not the origin.
 Remember, any whole number may be placed over 1; for example, 3 is
really
 If the slope is positive, you will have
 If the slope is negative, you will have
↑
→
↓
→
EXAMPLE: GRAPH
𝟓
𝒚 = − 𝒙 + 𝟒 using the slope-intercept method
𝟑
STEP ONE: From the origin, you would go up (on the y-axis) 4 points. Plot
the point (0,4)
STEP 2: Then stop to look at the slope: the slope is − .
WHEN the slope is negative, it is easier to ‘use’ the negative in the
numerator.
STEP 3: SLOPE: FROM the point on the y-axis (0,4) go down 5 points
(this takes care of the negative), STOP (do not make a point) and then go 3
points to the right. Make a point at (3, −1).
Now, you have 2 points: (0, 4) 𝑎𝑛𝑑 (3, −1)
STEP 4: CONNECT the points with a smooth, continuous line.
EXAMPLE:
𝒚 = 𝟒𝒙 − 𝟐
STEP 2: Then stop to look at the slope. The slope is POSITIVE
𝟒
4, 𝑤ℎ𝑖𝑐ℎ 𝑖𝑠 .
𝟏
STEP 3: SLOPE: FROM the point on the y-axis (0, −2) go up 4 points
(because the slope (4) is positive), stop (do not make a point) and then go 1
point to the right. Make a point (1, 2).
STEP 4: Connect the points with a smooth, continuous line.