Question

Complete the equation of the line through (-1,6) and (,7-2)

Answer 1

The two points given are

A(-1, 6)

B(7, -2)

We shall start by calculating the slope of the line, since we've been given two points.

`\begin{gathered} \text{The slope which is m, is derived as;} \\ m=(y_2-y_1)/(x_2-x_1) \\ m=(-2-6)/(7-\lbrack-1\rbrack) \\ m=(-8)/(7+1) \\ m=(-8)/(8) \\ m=-1 \end{gathered}`

Next we shall derive the y-intercept, by inserting the known values into the equation in slope-intercept form.

`\begin{gathered} y=mx+b \\ We\text{ shall use the first set of coordinates, that is (-1, 6)} \\ 6=-1(-1)+b \\ 6=1+b \\ 6-1=b \\ b=5 \end{gathered}`

Having calculated the values of m (the slope) and b (the y-intercept), the equation is now;

`\begin{gathered} y=mx+b \\ y=-1x+5 \\ y=-x+5 \end{gathered}`