practice finals/equations of lines

[S.Hobden]

Find the equations of 2 distinct lines that intersect at the point (5,8)
How do you check that the only point of intersection is (5,8)

..practice exams always seem to have questions that our class hasnt been taught..

 

[Matt]

To write the equation of a line, you need:

(1) a point on the line
(2) the slope of the line

A point on the line has already been given to you. Hence, to make two different lines, you need two different slopes.

 

[steve_b]

To answer your question:

"How do you check that the only point of intersection is (5,8) "

First, two straight lines can only intersect at one point, so you can substitute the values x=5 and y=8 into both equations and see if you get true statements.

As an alternative, you can solve the equations "simultaneously" by your favorite method (substitution, elimination, Cramer's Rule, etc) and see what values of x and y come up.

Steve