Question

without graphing, determine the equation whose graph intersects the graph of -6x + 3y = 11 exactly once. how do i get my answer?

Answer 1

What are the choices?

Answer 2

find any point on this line
let x=0
y=11/3
we want the other line to pass through this point, and make sur it doesn't overlap the given line
find the slope of this line
3y=6x+11
y=2x+11/3
y=mx+c
m=slope
c= intercept on y axis
given line's slope is 2
let the slope of other line be anything but 2
say 1
y=mx+c
m=1
y=x+c
it passes through the point (0, 11/3) ( we found this earlier)
y=x+11/3
this is the required line, we can find many lines like these

Answer 3

First convert from standard form to slope\intercept form: \[y=mx+b\] in your case: \[y=2x+\frac{11}3\]
1. If you have 2 equivalent equations in standard form...i.e. infinite common points ... In slope intercept form both equations will look exactly the same.

2. If in slope\intercept form they have the same value for the slope(m) but different y-intercept(b) ... the the 2 lines are parallel ... i.e 0 points of intersection.

3. If the two lines have different slopes(m) then they MUST intersect exactly once.