Question

find the equation of the line passing through the given points A/a(-2,-4) & b(-1,5)
b/ c(2,-4) & d(-1,5). ?

Answer 1

Solution to part A
\[y-(-4)=\frac{-4-5}{-2-(-1)}(x-(-2))\]\[\implies y+4=\frac{9}{1}(x+2)\]\[\implies y+4=9x+18\implies y=9x+14\]

Answer 2

First find the slope:\[m = \frac{\Delta y}{\Delta x} = \frac{y_{2}-y_{1}}{x_{2}-x_{1}} = \frac{5 - (-4)}{(-1)-(-2)} = \frac{9}{1} = 9\]
Then, using the given points and the slope, plug them in to the point-slope formula:\[(y - y_{1}) = m(x-x_{1})\]\[[y-(-4)] = 9[x-(-2)]\]\[y+4 = 9(x+2)\]You can then simplify it into slope-intercept form:\[y +4 = 9x+18\]\[y = 9x+14\]