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Straight Lines

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**I. Graphing Straight Lines**

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1. Horizontal Line y = c Example: y = 5 We graph a line through the point (0,c), for this example, the point (0,5), parallel to the x axis

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2. Vertical Line x = c Example: x = 5 We graph a line through the point (c,0), for this example, the point (5,0), parallel to the y axis

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3. Line through the Origin y = cx Example: y = 2x We find one more point by letting x be any real number, for example x = 5. In this example if x = 5 then y = 2(5)=10. Thus the line is also through (5,10). We join (0,0) and (5,10) and extend in both directions.

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4. Line intersecting both Axes y = ax+ b Example: y = 2x +10 We find the points of intersection with the axes, by first letting x = 0 and find y ( in this example, we get y = 10), then letting y = 0 and find x ( in this example, we get x = - 5). We plot the resulting two points, in this example, the points: (0,10) and (-5,0), and extend.

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**II. Intersection of Straight Lines**

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Example (1)

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Graph the lines represented by the equations ( Notice that we have distinct lines with distinct slopes; thus they intersect at exactly one point)

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To Find the point of intersection of two lines , which is here (2,1), we solve the system of linear equations defining these lines

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**Four methods of solving systems of two Linear equations of two variables**

1. Algebraic Method a. Elimination by Substitution b. Elimination by Addition 2. Matrix Reduction Method 3. Using the inverse of a matrix 4. Cramer’s Rule

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The Algebraic Method

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Homework

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