Question

Find the equation of the line through the points (3,6) and (-1, 1).

Answer 1

Let's begin by listing out the information given to us:

(x, y) at point 1 = (3, 6)

(x, y) at point 2 = (-1, 1)

The equation of a straight line is given by:

`\begin{gathered} y=mx+b \\ m=(y_2-y_1)/(x_2-x_1)=(1-6)/(-1-3)=(-5)/(-4) \\ m=(5)/(4) \end{gathered}`

Substitute the slope (m) into the equation, we have:

`\begin{gathered} y=mx+b \\ m=(5)/(4) \\ y=(5)/(4)x+b \\ \text{Substitute the value of x \& y into the equation from (}3,6)​ \\ 6=(5)/(4)\cdot3+b\Rightarrow6=(15)/(4)+b \\ b=6-(15)/(4)=6-3(3)/(4) \\ b=2(1)/(4)=2.25 \\ \\ \therefore y=(5)/(4)x+2.25 \end{gathered}`