Question

a line that passes through (1, 7), (10, 1)

Answer 1

The slope-point form: y = mx + b

m-the slope:    $m=\dfrac{y_2-y_1}{x_2-x_1}$

$(1;\ 7)\to x_1=1\ and\ y_1=7\\(10;\ 1)\to x_2=10\ and\ y_2=1$

subtitute

$m=\dfrac{1-7}{10-1}=\dfrac{-6}{9}=-\dfrac{2}{3}$

The slope-point form: $y-y_1=m(x-x_1)$

subtitute

$y-7=-\dfrac{2}{3}(x-1)\\\\y-7=-\dfrac{2}{3}x+\dfrac{2}{3}\ \ \ |add\ 7\ to\ both\ sides\\\\\boxed{y=-\frac{2}{3}x+7\frac{2}{3}}$