Presentation on theme: "Writing Equations from Word Problems"— Presentation transcript:
1Writing Equations from Word Problems 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?
2RECAPSlope 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)
3Learning 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 - 51 = 3(2) + b1 = 6 + b= b
4Learning 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.
5Example: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 -32-3 = -1y = mx + b (Doesn’t matter which point you choose to plug in)1 = -3(3) + b1 = -9 + b10 = b3. 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)
6Word ProblemsWhat 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.
7Example: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.