"Each coefficient [is] twice the value of its constant" I interpret as:
y=2aix+ai, where ai is the constant of the i-th equation (i is between 1 and 5). ai is also the y-intercept.
Or perhaps "Each [y-]coefficient [is] twice the value of its constant and each x variable [is] t[h]rice the value of its [y-]coefficient" meaning:
2aiy-6aix-ai=0, which is the same as:
2aiy=6aix+ai. (If the y-coefficient is 2ai, then thrice this coefficient is 6ai.)
Neither of these interpretations leads to linear equations starting at or passing through the origin (0,0), so we're looking at what "point of origin" could mean. It could mean that all the linear equations intersect at one point which is taken to be the point of origin. But see below.
1.1 y=(6aix+ai)/(2ai)=3x+½ so there is only one actual equation, because the coefficients cancel out. So this is just a straight line.
More attempts to interpret to follow...
There's no more information in the question so I assume the value of each ai is arbitrary.
Below is my best interpretation of this problem.
Table of values used to draw the graph:
β0 |
1 |
2 |
3 |
4 |
5 |
β1 |
2 |
4 |
6 |
8 |
10 |
data value x |
3 |
6 |
9 |
12 |
15 |
y= |
1+2x |
2+4x |
3+6x |
4+8x |
5+10x |
Point on line |
F(3,7) green |
G(6,26) blue |
H(9,57) red |
I(12,100) orange |
J(15,155) purple |
Points A(0,1), B(0,2), C(0,3), D(0,4), E(0,5) are the intercepts or constants.
Note that all lines intersect at (-0.5,0).