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?

Question

asked Nov 9, 2020 204k views

2 Answers

Vork · Answer 1 · 2020-11-15T20:52:37+0000

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.