SOLUTION: The equations y = 2x - 1 and y = -1/2x + 4 intersect in Quadrant I. Find the area of the triangle formed with this point of intersection and the two y-intercepts of the lines.

Question 1050683: The equations y = 2x - 1 and y = -1/2x + 4 intersect in Quadrant I. Find the area of the triangle formed with this point of intersection and the two y-intercepts of the lines.
Found 3 solutions by ewatrrr, Fombitz, josmiceli:
Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!

A = (1/2)bh
A = (1/2)5*2 = 5 units^2

Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!
Graphically,
.
.
.
.
.
.
.
The y intercepts are -1 and 4 respectively so the base of the triangle is
The height of the triangle is .
You can also find this using the intersection point of the two lines by setting them equal to each other,

So,

Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Find the point of intersection

---------------------
By substitution:

Multiply both sides by

and

----------------------------
The intersection is at ( 2,3 )
----------------------------
Now find the y-intercepts
by setting
-----------------------------

( 0, -1 )
----------------

( 0, 4 }
--------------------
The distance between the 2 y-intercepts is:

-------------------
The height of the triangle formed is
the x-value of the intersection ( 2,3 )
which is
---------------------

The area is 5 square units
------------------------
Here's the plot of the lines:

RELATED QUESTIONS
I'm supposed to put the following formulas in y=mx+b form. Then I'm supposed to plot the (answered by jim_thompson5910)
A right triangle is formed in the 1st quadrant. It has vertices at A(0,0), B(0,y), and... (answered by solver91311)
Determine whether the pair of lines y = 2x + 1 and x - y = 5 are parallel or intersect.... (answered by fractalier,Fombitz)
Hi! could you please help me with this question? how do you sketch the graph of these... (answered by poliphob3.14)
The line x/3 + y/4 = 1 forms a triangle with the x and y axes in the first quadrant.... (answered by greenestamps,robertb)
The lines x-y-2=0 and 2x-5y-7=0 intersect at point P. Find co-ordinates of point P. The... (answered by anand429)
a straight line with slope -5 contains the point (1, 2). What is the area of the triangle (answered by solver91311)
a straight line with slope -5 contains the point (1, 2). What is the area of the triangle (answered by Alan3354)
the lines y=3x+4 and y=2x+6 intersect at point m. line n goes through point m and is... (answered by josgarithmetic)