Question

Find the equation of a line that contains the points (3,4) and (-6,5). Write the answer in slope intercept form

Answer 1

Given:

`(3,4)\text{ and }(-6,5)`

Using the formula;

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

where;

`\begin{gathered} x_1=3,y_1=4 \\ x_2=-6,y_2=5 \end{gathered}`

Hence,

`\begin{gathered} (y-y_1)/(x-x_1)=(y_2-y_1)/(x_2-x_1) \\ (y-4)/(x-3)=(5-4)/(-6-3) \\ (y-4)/(x-3)=(1)/(-9) \\ Cross\text{ multiplying;} \\ y-4=-(1)/(9)(x-3) \\ y-4=-(1)/(9)x+(1)/(3) \\ y=-(1)/(9)x+(1)/(3)+4 \\ y=-(1)/(9)x+4(1)/(3) \\ y=-(1)/(9)x+(13)/(3) \end{gathered}`

Therefore, the equation of the line in slope-intercept form is;

`y=-(1)/(9)x+(13)/(3)`