Question

what are the correct steps in finding the linear equation of a line that passes threw the points (-1,7) and (2,4) using the point slope form method?

Answer 1

We have to find the equation of a line fo which we know two points, using the point-slope form.

The point-slope let us write the equation of the line knowing the value of the slope m and the coordinates of one point (x0,y0) of the line:

$y-y_0=m(x-x_0)$

We use the two known points to calculate the slope m:

$m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{4-7}{2-(-1)}=\frac{-3}{3}=-1$

Using the point (-1,7), we can write the equation as:

$\begin{gathered} m=-1 \\ (x_0,y_0)=(-1,7) \\ \\ y-7=-1\cdot(x-(-1)) \\ y-7=-(x+1) \\ y-7=-x-1 \\ y=-x-1+7 \\ y=-x+6 \end{gathered}$

Answer: From the options, the right ones are:

y-7=-1(x-(-1))

y-4=-1(x-2) --> this one would have been used if we picked the point (2,4) instead of (-1,7)

y=-x+6