Finding the Rule of a Line

A straight line always follows the RULE

y = mx + b

m is the slopeb is the y-intercept

Where;

y is a y-coordinatex is an x-coordinate

Standard to Function

• 2x + y = 5 2y = 5x -6

• -4x + y = 8 x -2y = 105

Steps to solving Linear Functions

1. Determine x (independent) and y (dependant) Hint: Words

2. Determine a (slope or rate) and b (y-int or initital value) Hint: Values

3. Write the rule of the function if the form y=ax+b Example: y = 2x + 10

4. Solve the question. Can now plug any value in for x and solve y or plug any value for y and solve x.

x y

x y

x y

x y

x y-2 -10 02 1

y 12x

x y-2 -30 -22 -1

y 12x 2

y 12x 4

x y-2 -50 -42 -3

y 12x 2

x y-2 10 22 3

2. Changing the y-intercept (b)

b translates the line vertically (up or down).

Steps to Finding the RULE given 2 points

Step 1: Find the slope using a= y2-y1

x2-x1

Step 2: Find the y-intercept (b) by plugging an (x,y) coordinate into y=ax+b

Step 3: State the final equation.

Sketch to verify your answer

Step 3: Final equation

Find the equation of the line going through (-6,5) & (-4, 6)

Step 1: Find a

a = x2-x1

y2-y1

= (6) - (5) (-4) - (-6)

a = 12

Step 2: Find b using (-6,5)

y=ax + b

(5) = 12 (-6) + b

(5) = -3 + b+3 +3

b = 8

y= 1 2

x + 8

Step 3: Final equation

Find the equation of the line going through (-2,6) & (1, 3)

Step 1: Find a

a = x2-x1

y2-y1

= (3) - (6) (1) - (-2)

a = -33

Step 2: Find b using (1,3)

y=ax + b

(3) =-1(1) + b

(3) = -1 + b+1 +1

4 = b

y= -1x + 4 a = -1