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=- What is the value of b?

Answer 1

5

Explanation:

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Answer 2

The value of
`m= (- 1)/(6)` and
`b = 5`

Solution:

Given, Line passes through points
`A(-6,6) = (x_1, y_1); \ B(12,3) = (x_2 , y_2)`

Slope of line passing through two points is
`m = ((y_2-y_1))/((x_2-x_1))`

`\rightarrow ((3-6))/((12- (-6)))`

`\rightarrow (-3)/(18) = (-1)/(6)`

Equation of a straight line passing through point-slope form is
`y - y1 = m (x - x1) --- (1)`

Since we have two points we can use any point. Let us take
`A (-6,6)` and m
`(-1)/(6)` and substitute in (1)

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

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

`\Rightarrow y = (-1)/(6x + 5)` [By equating as
`y = mx + b`]

`m = (-1)/(6) ; b = 5`

Substituting the other coordinates also gives the same result.