Question

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

(1, 1), (3, − 1/5)

Answer 1

`The\ slope-intercept\ form:y=mx+b\\\\The\ slope-point\ form:y-y_1=m(x-x_1)\\\\m=(y_2-y_1)/(x_2-x_1)`


`(1;\ 1)\to x_1=1;\ y_1=1\\\left(3;-(1)/(5)\right)\to x_2=3;\ y_2=-(1)/(5).\\\\Subtitute:\\\\m=(-(1)/(5)-1)/(3-1)=(-1(1)/(5))/(2)=-((6)/(5))/(2)=-(\\ot6^3)/(5)\cdot(1)/(\\ot2_1)=-(3)/(5)`



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