Straight Lines

I. Graphing Straight Lines

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

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

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.

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.

II. Intersection of Straight Lines

Example (1)

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

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

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

The Algebraic Method

Homework