1. By Matty Lu and Mc-Welch
Linear Equations
By Matty Lu and Mc-Welch

2. Basics Slope-Intercept Form y = mx + b m = slope b = y-intercept
Ex. y = 2/3x + 2
slope = 2/3
y-intercept = 2

3. Slope y = mx + b slope= rise/run slope = y = y2-y1 x x2-x1
Ex. (-3,0) (3,4)
slope= = 2
3-(-3) 3

4. y-intercept y = mx + b Ex. (3,4) m= 2/3 4=(2/3)(3) + b 4 = 2 + b 2 = b
b = x-value at which line crosses y-axis
Plug in coordinates for x and y
Plug in slope for m
Solve for b
Ex. (3,4) m= 2/3
4=(2/3)(3) + b
4 = 2 + b
2 = b

5. Example 1
Write in slope-intercept form the equation of the line that passes through the given points.
Ex (6,2) , (8,-4)
Step –2 = -3
8 - 6
Final Step y = mx + b
y = -3x + 20
Step 2 y = mx + b
2 = (-3)6 + b
b = 20

6. Example 2
Using the graph, identify y-intercept and slope and put into slope-intercept form
y-intercept = 1
slope = -4
y = -4x + 1

7. Example 3
Between , a company’s profits decreased by about $1200 per year. In 1997, the company had an annual profit of $1,500,000. Write an equation that gives the annual profit P in terms of the year t. Let t=0 represent 1995.

8. Example 3 (cont.) Step 1: Identify key values Step 3: Write equation
x = years (t) y = $profit (P)
slope = -$1200/yr
point (2, ) with 2 representing the year 1997
Step 3: Write equation
y = mx + b
y = -1200x
Step 2: Substitute values into equation, and solve for b
y = mx + b
= (-1200)(2) + b
b =

9. Extra Problems Write equation using the Click for the answers.
given information.
m = 4, b = -2
m = -5, b = 3
(2, 6), m = 2
4. (3, -9), m = -5
5. (-2, 5), (2, 4)
6. (9, -1), (1, -9)
Click for the answers.
1. y = 4x – 2
2. y = -5x + 3
3. y = 2x + 2
4. y = -5x + 6
5. y = -1/4x + 9/2
6. y = x – 10

10. Website Links - explanations
For additional practice go to the following website,