Answer:
B.
Step-by-step explanation:
I think I'm going to go with the plug in method here.
If you get the same value on both sides, then the point is contained on the line.
A)
4x-y=-6
Test (-1,2): 4(-1)-2=-6
4(-1)-2=-6
-4-2=-6
-6=-6
True; the equation holds for (-1,2).
Test (3,1): 4(3)-1=-6
4(3)-1=-6
12-1=-6
11=-6
False; the equation doesn't hold for (3,1).
A isn't the right choice.
B)
x+4y=7
Test (-1,2): -1+4(2)=7
-1+4(2)=7
-1+8=7
7=7
True, the equation holds for (-1,2).
Test (3,1): 3+4(1)=7
3+4(1)=7
3+4=7
7=7
True, the equation holds for (3,1).
Since the equation held for both (-1,2) and (3,1) then B is the right answer.
-------------------Let's also go ahead and find the equation another way:
(3,1) and (1,-2) are points on your line.
I'm going to write an equation for these points in slope-intercept form first which is y=mx+b where m is slope and b is y-intercept.
I will then rearrange into standard form like your choices are in.
m=slope=rise/run.
To find this, I like to line up the points and subtract and then put 2nd difference over 1st difference.
Like so:
(-1,2)
-(3,1)
---------
-4 1
The slope is 1/-4 or -1/4.
So the equation so far is y=-1/4 x+b since m=-1/4.
Now to find b, I'm going to use y=-1/4 x +b along with one of the given points on the line like (x,y)=(-1,2).
y=-1/4 x+b
2=-1/4 (-1)+b
2=1/4+b
Subtract 1/4 on both sides:
2-1/4=b
7/4=b
So the equation of the line is y=-1/4 x +7/4.
Now the goal is to write in ax+by=c form where a,b,c are integers.
Multiply both sides of y= -1/4 x +7/4 by 4 giving you:
4y=-1x+7
Add 1x on both sides:
1x+4y=7
or
x+4y=7 since 1x=x
So x+4y=7 is the answer if you prefer this way. Well anyway you prefer, this is the correct standard form for this line.
