CST 504 Standard and Function Form of a Line
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Transcript of CST 504 Standard and Function Form of a Line
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Finding the Rule of a Line
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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
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Standard to Function
• 2x + y = 5 2y = 5x -6
• -4x + y = 8 x -2y = 105
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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.
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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).
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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
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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
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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