# Writing Equations from Word Problems

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Writing Equations from Word Problems
What are my two unknowns? X will be the independent variable, y will be dependent 2. Look for key words to tell you operations. Orange reference sheet may help. 3. The constant rate of change will be the slope. The value of x at 0 will be the y-intercept. 4. Write an equation and test it. Does it make sense? Will it work every time?

RECAP Slope intercept form: y = mx + b We know how to: -write an equation given slope and y – intercept -write an equation given a graph -write an equation from a word problem (slope and y intercept)

Learning Target 2: Write an equation given slope and a point or two points.
Use y = mx + b and fill in what you know! Solve for the unknown y intercept. Plug original slope and y-intercept back into equation. Example: Write an equation of a line that passes through (2,1) with a slope of 3. y = mx + b 3. y = 3x - 5 1 = 3(2) + b 1 = 6 + b = b

Learning Target 2: Write an equation given slope and a point or two points.
Given two points: Find the slope of the two points. Use the slope and one of the points to plug into y=mx + b. Solve for the y – intercept. Plug the slope and y –intercept you found into y = mx + b.

Example: Write an equation of the line that passes through each pair of points. (3, 1) and (2, 4) 4-1 = 3 The slope is equal to -3 2-3 = -1 y = mx + b (Doesn’t matter which point you choose to plug in) 1 = -3(3) + b 1 = -9 + b 10 = b 3. y = -3x + 10 – If asked to write in a different form, you can always rewrite. Standard Form: 3x + y = 10 (add 3x to both sides to get on the same side as y)

Word Problems What are the independent/dependent variables? These are your x and y values. The problem will give you the slope and a point or two points. The slope is a rate of change, which stays constant at all times. Use the information from the problem to plug back into y = mx + b.

Example: Greg is driving a remote control car at a constant speed. He starts the timer when the car is 5 feet away. After 2 seconds, the car is 35 feet away. Constant speed (feet per second) is a constant rate, so it is the slope. Seconds, or time is our independent variable (x). Feet, or distance is our dependent variable (y). When he starts the timer, no time has passed (when x is 0), but the car is 5 feet away. This would be the ordered pair (0, 5). After 2 seconds, the car is 35 feet away. This would be the ordered pair (2, 35). Find the slope of the two points, and then solve for the y-intercept.

HOMEWORK Pg : 11 – 33 odds only, 39, 40-42

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