Which equation represents the line that passes through the points (4, 6) and (−2, −1)? Select one:highlight_offhighlight_offhighlight_offhighlight_off

To find the equation of the line that passes through the points (4, 6) and (-2, -1), we first need to find the slope (m) of the line. The formula for the slope is:

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

where (x1, y1) and (x2, y2) are the coordinates of the two points.

Substituting the given points into the formula, we get:

m = (-1 - 6) / (-2 - 4) = 7 / -6 = -7/6

Now that we have the slope, we can use the point-slope form of the equation of a line to find the equation of the line. The point-slope form is:

y - y1 = m(x - x1)

Substituting the slope and one of the points into the formula, we get:

y - 6 = -7/6 (x - 4)

This simplifies to:

y - 6 = -7/6x + 14/3

Adding 6 to both sides gives the final equation of the line:

y = -7/6x + 32/3

So, the equation of the line that passes through the points (4, 6) and (-2, -1) is y = -7/6x + 32/3.