SOLUTION: a straight line with slope -5 contains the point (1, 2). What is the area of the triangle formed by this line and the x- and y-axes?

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Question 989478: a straight line with slope -5 contains the point (1, 2). What is the area of the triangle formed by this line and the x- and y-axes?
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Find the standard form equation of the line. First use the Point-Slope form:



where are the coordinates of the given point and is the given slope.





Now find the and intercepts.

Substitute 0 for :



Substitute 0 for :



So the intercepts are and

One of the angles of the triangle is the intersection of the axes, hence is a right angle. So one leg of the triangle is the distance from the origin to one of the intercepts and the other leg is the distance from the origin to the other intercept, which is to say: and .

The area of a right triangle is one-half of the product of the measures of the two legs.

John

My calculator said it, I believe it, that settles it