Question

Which system of equations is represented by the following graph?

a graph of two intersecting lines on a coordinate plane. One passes through points (0, 3) and (6, 0). The other passes through points (0, −3) and (3, 0).

x − 2y = 6
x + y = 3
y = x + 3
y = −1 over 2x + 3
y = x − 3
y =1 over 2x + 3
x + 2y = 6
x − y = 3

Answer 1

any idea ?

Answer 2

A?

Answer 3

find the equation of the lines
1- find the slope of the line
slope(m)= (y2-y1)/(x2-x1)
m=(0-3)/(6-0)=-3/6=-1/2

Answer 4

2- find the equation
y-y1=m(x-1) pick any points of the two
y-0=-1/2(x-6)
y=-1/2x+3
multiply both sides by 2
2y=-x+6
x+2y=6 this is the first equation

Answer 5

the second equation
m=(0-(-3))/(3-0)=3/3=1
y-y1=m(x-x1) using second point
y-0=1(x-3)
y=x-3 this is the second equation

Answer 6

-x+y=-3
multiply both sides by -1
x-y=3

Answer 7

the answer is D

Answer 8

You can get it by moving backwards. Check the system that satisfy the points while replacing their coordinates :)