Writing Equations 10/17/2017.

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Presentation transcript:

Writing Equations 10/17/2017

Writing an Equation Given Two Points

When given two points Use slope formula to find slope Substitute slope and one point into point-slope form Simplify and solve for ‘y’

Example Find an equation of the line through (–4, 0) and (6, –1). Write the equation in slope- intercept. First, find the slope. Continued

Example (cont) Now substitute the slope and one of the points into the point-slope form of an equation. 𝑦=− 1 10 (𝑥−(−4)) 𝑦=− 1 10 (𝑥+4) 𝑦= −𝑥 10 − 2 5

Your turn Find the equation of the line that passes through the points (3, 2) and (5, 6) Find the equation of the line that passes through the points (2, 3) and (-1, -1)

Finding Equations of Vertical and Horizontal Lines

Example Find an equation of the vertical line through (–7, –2). The equation of a vertical line can be written in the form x = c, so an equation for a vertical line passing through (–7, –2) is x = –7.

Example Find an equation of the line parallel to the line y = –3 and passing through (10, 4). Since the graph of y = –3 is a horizontal line, any line parallel to it is also horizontal. The equation of a horizontal line can be written in the form y = c. An equation for the horizontal line passing through (10, 4) is y = 4.

Putting it all together In 1997, Window World , Inc. had 50 employees. In 2012, the company had 85 employees. Let x represent the number of years after 1997 and let y represent the number of employees. a.) Assume that the relationship between years and number of employees is linear, write an equation describing this relationship. b.) Use the equation to predict the number of employees in 2007. Continued

Example (cont) Continued a. The year 1997 is represented by x = 0. 2012 is 15 year after 1997, so 2012 is represented by x = 15. The two points (0, 50) and (15, 85) will be used to find the equation. Substitute the values for m, x1, and y1. Distribute. Add 50 to both sides. Continued

Example (cont) Use the equation to predict the number of employees in 2007. In 2007, x = 10.

ON you graph paper A rock is dropped from a 400ft cliff. After 1 second the rock is traveling at 32ft/s. after 3 seconds the rock is traveling at 96ft/s Assume the relationship between time and speed is linear. Write an equation describing this relationship. (time, speed) Use this equation to determine the speed of the rock after 4 seconds Graph the equation. A certain chain of books stores is slowly closing down stores. Suppose that on 2006 there were 3991 stores and in 2010 there were 3200 stores. Write an equation describing the relationship between time and number of stores. (# of years, stores) Use the equation to predict the number of stores in 2018. Graph the equation.