First, we must determine the slope of the line passing through these two points. The slope can be found by using the formula: #m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))#
Where #m# is the slope and (#color(blue)(x_1, y_1)#) and (#color(red)(x_2, y_2)#) are the two points on the line.
Substituting the values from the points in the problem gives:
#m = (color(red)(7) - color(blue)(-41))/(color(red)(-25) - color(blue)(91)) = (color(red)(7) + color(blue)(41))/(color(red)(-25) - color(blue)(91)) = 48/(-116) = (4 xx 12)/(4 xx 29) = (color(red)(cancel(color(black)(4))) xx 12)/(color(red)(cancel(color(black)(4))) xx -29)#
#m = -12/29#
Now, use the point-slope formula to find an equation for the line passing through the two points. The point-slope formula states: #(y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))#
Where #color(blue)(m)# is the slope and #color(red)(((x_1, y_1)))# is a point the line passes through.
Substituting the slope we calculated and the first point gives:
#(y - color(red)(-41)) = color(blue)(-12/29)(x - color(red)(91))#
#(y + color(red)(41)) = color(blue)(-12/29)(x - color(red)(91))#
We can also substitute the slope we calculated and the second point giving:
#(y - color(red)(7)) = color(blue)(-12/29)(x - color(red)(-25))#
#(y - color(red)(7)) = color(blue)(-12/29)(x + color(red)(25))#
