Question

Write the equation of the line that passes through the points (6,5) and (-7,4). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.

Answer 1

The general form of the equation of a line in point-slope form is:

y - y1 = m(x -x1)

Where "m" is the slope and.

The slope of a line is given by the following formula:

`m=(y2-y1)/(x2-x1)`

Where (x1,y1) and (x2,y2) are two points where the line passes through.

In this case, we are given the points (6,5) and (-7,4), then we get:

`m=(4-5)/(-7-6)=(-1)/(-13)=(1)/(13)`

By replacing 1/13 for m, 6 for x1 and 5 for y1 into the equation of a line in point-slope form, we get:

`y-5=(1)/(13)(x-6)`