Examples of graphs linear equations in two variables parallel intersecting and coinciding
Answers
Answer:
Step-by-step explanation:
Intersecting Lines
If two lines have different slopes, then definitely they will meet at a certain point. You can imagine this by drawing two line segments that are not parallel on a board (the intersection may be outside the board). If you extend the two segments on one side, they will definitely meet at some point as shown below. The extension of the line segments are represented by the dashed lines.
intersecting lines
Therefore, if two lines on the same plane have different slopes, they are intersecting lines.
Exercise: Give equations of lines that intersect the following lines.
y = 7x + 2
3x + 8y – 7 = 0
Coinciding Lines
As discussed above, lines with the same equation are practically the same line. Therefore, to be able to distinguish coinciding lines using equations, you have to transform their equation to the same form (e.g. slope-intercept form). For example, the lines 3x + y = 5 and 3x = 5 – y are coinciding lines because they both can be transformed to y = -3x + 5. So, if two equations can be transformed to one form and they are equal, they are coinciding lines.