Question

Line AB passes through points A(–6, 6) and B(12, 3). If the equation of the line is written in slope-intercept form, y = mx + b, then m = – and b =

Answer 1

Slope = (6-3) / -6-12) = 3 / -18 = -1/6

y = -1/6 x + b

Plug in x = -6 and y = 6 to find the value of b:-

6 = -1/6*-6 + b
b = 6-1 = 5

So the answer is m = -1/6 and b = 5

Answer 2

Answer: The required slope-intercept f the line AB is
`y=-(1)/(6)x+5,`

where
`m=-(1)/(6)` and c = 5.

Step-by-step explanation: Given that a line AB passes through points A(–6, 6) and B(12, 3).

We are to find the equation of the line in slope-intercept form, y = mx + c.

The line AB passes through the points A(-6, 6) and B(12, 3), so the slope of the line AB will be

`m=(3-6)/(12-(-6))=(-3)/(18)=-(1)/(6).`

Also, since A(6, -6) is a point on the line AB, so the equation of the line is given by

`y-6=-(1)/(6)(x-(-6))\\\\\\\Rightarrow y-6=-(1)/(6)(x+6)\\\\\\\Rightarrow y-6=-(1)/(6)x-1\\\\\\\Rightarrow y=-(1)/(6)x-1+6\\\\\\\Rightarrow y=-(1)/(6)x+5.`

Thus, the required slope-intercept f the line AB is
`y=-(1)/(6)x+5,`

where
`m=-(1)/(6)` and c = 5.