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,

Answer 1

The value of $m= \frac{- 1}{6}$ 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 $m = \frac{(y_2-y_1)}{(x_2-x_1)}$

$\rightarrow \frac{(3-6)}{(12- (-6))}$

$\rightarrow \frac{-3}{18} = \frac{-1}{6}$

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 $\frac{-1}{6}$ and substitute in (1)

$\Rightarrow y - 6 = \frac{-1}{6 (x - (-6))}$

$\Rightarrow y - 6 = \frac{-1}{6x -1}$

$\Rightarrow y = \frac{-1}{6x + 5}$ [By equating as $y = mx + b$]

$m = \frac{-1}{6} ; b = 5$

Substituting the other coordinates also gives the same result.