Need Help With Linear Equations

Question

I need help with this question: a family of lines have equations of the form y=-2x+c, where x is a positive number. Let O denote the origin, and let A and B be the x axis and y axis intercepts of y=-2x+c. If the triangle AOB has area 4, find the value of c.

Answer 1

"the triangle AOB"

A(c/2,0) [point where y=0; so x=c/2]

O(0,0) [origin]

B(0,c) [point where x=0]

Area: [(1/2)bh]

(1/2)(c/2)(c) = 4

(1/4)c² = 4

c² = 16

c = 4

The value of c is 4.

Check: the line is y=-2x+4

[x intercept] (2,0)

[Origin] (0,0)

[y intercept] (0,4)

Area = 4