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Question

the graph passes through (6,1) and the x intercept is twice the y intercept. write in form of y=mx+b

Answer 1

We want the form y=mx+b
1) The x intercept is twice the y intercept i.e.
-b/m = 2b
i.e. 2b + b/m = 0
i.e. b(2m+1)=0
i.e. 2m+1=0
i.e. m=-1/2
2) The graph passes through (6,1) i.e. when x=6, y=1
i.e. 1=6m+b
i.e. 1=6(-1/2)+b
i.e. 1=-3+b
i.e. b=4

Hence, the graph is: y=-1/2x+4

Answer 2

Because you know that the x intercept is twice the y intercept you know that the slope is equal to (-1/2) you can find this by doing the rise (in this case it is acutally down) over the run. I just assumed values for the intercepts y=1 and x = 2. So just put a dot at (0,1) and (2,0) and connect them and this will give you the slope of your line. Then you can find where your line which passes through the point (6,1) will pass through the y axis. So now just put into y=mx + b to find b.
m = slope of line = -1/2 y=1 and x = 6
1 = (-1/2) 6 +b so b = 4
so, y = (-1/2)x + 4

Answer 3

From the point we know that 1=6m+b.
At the x intercept, y=0, so mx = -b or x = -b/m
At the y intercept, x=0, so y = b
From the problem x =2 y or - b/m = 2 b
So -b = 2bm or m= -1/2
So 1= -3+ b and b= 4.
Then y = -x/2 + 4

Answer 4

If the x-intercept is twice the y-intercept, then the line has a slope of -1/2

So writing the equation...

(y - 1) / (x - 6 ) = -1/2

Cross Multiply

2y - 2 = -x + 6

Solve for y

2y = -x + 8

y = -1/2 x + 4

Answer 5

when y = 0, mx + b = 0, mx = -b, x = -b/m. this is x intercept
when x = 0, y = b. this is y intercept

so -b/m = 2b, -b/2b = m, m = -1/2.

then y = (-1/2)x + b
1 = (-1/2)(6) + b
1 = -3 + b
4 = b

so y = (-1/2)x + 4

Answer 6

x=6
y=1
:. 1=6m+b ------1
y intercept is b (x =0)
x intercept is -b/m (y=0)
x intercept is twice y intercept:
:. -b/m=2b
:.rearrange, m=-b/2b
which is negative half
sub back in first equation: b= 4
:. ANSWER: y= -1/2x + 4

Answer 7

The line must pass throug (0,y) and (2y,0).
The slope is -y/2y =-1/2.
Therefore, y=-1/2x+4.