Question

Find the slope-intercept form of the equation of the line passing through the given points.

Answer 1

$The\ slope-intercept\ form:y=mx+b\\\\The\ slope-point\ form:y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}$

$(1;\ 1)\to x_1=1;\ y_1=1\\\left(3;-\dfrac{1}{5}\right)\to x_2=3;\ y_2=-\dfrac{1}{5}.\\\\Subtitute:\\\\m=\dfrac{-\frac{1}{5}-1}{3-1}=\dfrac{-1\frac{1}{5}}{2}=-\dfrac{\frac{6}{5}}{2}=-\dfrac{\not6^3}{5}\cdot\dfrac{1}{\not2_1}=-\dfrac{3}{5}$


$y-1=-\dfrac{3}{5}\left(x-1\right)\\\\y-1=-\dfrac{3}{5}x+\dfrac{3}{5}\ \ \ \ |add\ 1\ to\ both\ sides\\\\\boxed{y=-\frac{3}{5}x+1\frac{3}{5}}$