3.6A Lines in the coordinate plane (Writing & classifying equations)

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Presentation transcript:

3.6A Lines in the coordinate plane (Writing & classifying equations) Geometry

We’ve learned to graph given an equation. Now we’ll learn to write the equation given the graph There are three ways. It all depends on what information you are given as to which process you use.

A.)Given the slope, m, and the y-intercept, b, use the equation y=mx+b Ex. 1 The y-intercept is -3 b=-3 The slope is 4/3 The equation is: y = x – 3 3 4

B.) If you are given slope, m, and a point (x1,y1) on the line Use Point Slope Form: y – y1 = m ( x – x1)

Ex. 2 Write an equation of a line containing the point (1,2) with slope of -1/2. Use (x1,y1) = (1,2) & m = -1/2 y – 2 = -1/2 ( x – 1) Now you can simplify to the slope intercept form y – 2 = -1/2 x + ½ y = -1/2 x + 5/2

C.) Given two points Use slope formula first. Then, either use point-slope formula or slope-intercept form twice.

Ex. 3 Given two points (-2,2) & (3,7) Find the slope: m=1 Plug this slope and one of the points into the point slope formula. y – 2 = 1 ( x – (-2)) y – 2 = x + 2 y = x + 4 (put the equation into slope intercept form) (3,7) (-2,2)

Classification of lines Parallel lines have same slope with different y-intercept. Intersecting lines have different slopes. Coinciding lines have same slope & same y-intercept. (IMS)

Ex. 4 Determine whether the lines are parallel, intersect or coincide. 6x - 12y = -24, 3y = 2x + 18 intersect

3-6B Writing equations of lines parallel or perp. Lines & graphs

Write equations of parallel or perpendicular lines Ex. 1 Write an equation of the line that passes through (-2,1) and is a.)parallel to y = -3x + 4

Ex. 1 Write an equation of the line that passes through (-2,1) and is b.) perpendicular to y = -3x + 4

Ex. 2 Write a model using slope-intercept form The number of U.S. cell phone subscribers increased from 16 million in 1993 to 44 million to 1996. Find the average rate of change and use it to estimate the number of subscribers in 1997.

Assignment

Ex. 6 Write a model using standard form You have $6 to spend on drinks and a salad at the school cafeteria. The drinks cost $1.25 each and the salad costs $.20 per ounce. Write an equation that models this situation. 1.25x+.20y=6

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