Question

Question Write an equation in slope-intercept form of the line that passes through (6, −2) and (12, 1)

Answer 1

`y = \frac 12x -5`

Explanation:

`\text{Given that,}~ (x_1,y_1) = (6,-2)~ \text{and}~ (x_2,y_2) = (12,1)\\\\\text{Slope,}~ m = (y_2 -y_1)/(x_2 -x_1) = (1+2)/(12-6)= (3)/(6) = \frac 12\\\\\text{Equation of line,}\\\\~~~~~~~~y-y_1 =m(x-x_1)\\\\\implies y+2=\frac 12 (x-6)~~~~~~~~~~~~~~;[\text{Point -slope form}]\\\\\implies y = \frac 12 x -3 -2\\\\\implies y = \frac 12x -5~~~~~~~~~~~~~~~~~~~~~;[\text{Slope-intercept form.}]`