Writing Equations of Lines

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Presentation transcript:

Writing Equations of Lines CG-L6 Objectives: To determine the slope y-intercept form of a line given various inputs. Learning Outcome B-4

Plot the following equations in Winplot, on the same screen. These equations are all in the form y = mx. What is m? Theory – Deriving the Equation of a Line

Plot the following equations in Winplot, on the same screen. These equations are all in the form y = mx + b (where m is 1). What is b? Theory – Deriving the Equation of a Line

Predict the line for each equation shown Predict the line for each equation shown. State slope & y-intercept for each case. Example 1 – Two Points

A Line is just a collection of points. The Slope, Y-Intercept Form of the Line describes a straight line with slope of m and y-intercept b. A Line is just a collection of points. The coordinates (x,y) of each point on the line will work in the equation (make the equation true). Find three points on each line shown: Example 1 – Two Points

(-1,1) (0,-2) (50,-49) Determine if the point is on the line. Example 1 – Two Points

The equations of horizontal and vertical lines look a little different The equations of horizontal and vertical lines look a little different. We can understand their equations by considering each to be collections of points, at a common distance from an axis. Horizontal Lines Vertical Lines Example 2 – Two Points (Special Case)

Write the equation for each line. Example 3 – Two Points (Special Case)

Write the equation for each line. Example 3 – Two Points (Special Case)

passes through slope y-intercept equation 4 1 -1/6 -3 (1,3) 2 Write equations in the form y = mx + b for the following straight lines. passes through slope y-intercept equation 4 1 -1/6 -3 (1,3) 2 (0,3) -1/2 (-3,-2) (0,1) (4,3) -1 (-1,0) 0 (5,6) undefined Example 4 – Given Slope, One Point

Write equations in the form y = mx + b for the following straight lines. (Hint: use the slope formula to find m, then substitute either point to find b) passes through and (-1,-2) (1,2) (-4,-4) (2,-1) Example 4 – Given Slope, One Point