Writing Equations from Word Problems

1. What are my two unknowns? - X will be the independent variable, y will be

dependent2. 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 + bWe 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.

Given slope and a point:1. Use y = mx + b and fill in what you know!2. Solve for the unknown y intercept.3. 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.

1. y = mx + b 3. y = 3x - 5 1 = 3(2) + b 1 = 6 + b2. -5 = b

Learning Target 2: Write an equation given slope and a point or two points.

Given two points:1.Find the slope of the two points.2.Use the slope and one of the points to plug

into y=mx + b.3.Solve for the y – intercept.4.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)1. 4-1 = 3 The slope is equal to -3

2-3 = -12. y = mx + b (Doesn’t matter which point you choose to plug in)

1 = -3(3) + b1 = -9 + b10 = 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

1. What are the independent/dependent variables? These are your x and y values.

2. 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.

3. 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. 227-228: 11 – 33 odds only, 39, 40-42