Question

Find the equation of a line that contains the points (3,7) and (−6,4). Write the equation in slope-intercept form, using fractions when required.

Answer 1

The equation of a line that passes throught two points is given as:

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

Plugging the values of the points given we have:

`\begin{gathered} y-7=(4-7)/(-6-3)(x-3) \\ y-7=(-3)/(-9)(x-3) \\ y-7=(1)/(3)(x-3) \\ y-7=(1)/(3)x-1 \\ y=(1)/(3)x-1+7 \\ y=(1)/(3)x+6 \end{gathered}`

Therefore the equation of the line in slope intercept form is:

`y=(1)/(3)x+6`