First, we need to determine the slope of the line. The formula for slope is:

#m = (color(blue)(y_2) - color(red)(y_1))/(color(blue)(x_2) - color(red)(x_1))#

Where: #(color(red)(x_1), color(red)(y_1))# and #(color(blue)(x_2), color(blue)(y_2))# are two different points on the line.

Substituting the values from the points in the problem gives:

#m = (color(blue)(1) - color(red)(-3))/(color(blue)(-1) - color(red)(-10)) = (color(blue)(1) + color(red)(3))/(color(blue)(-1) + color(red)(10)) = 4/9#

The point-slope formula is:

#(y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))#

Where: = #(color(red)(x_1), color(red)(y_1))# is a point on the line and #color(blue)(m)# is the slope of the line.

Substituting the slope we calculated and the values from the first point in the problem gives:

#(y - color(red)(-3)) = color(blue)(4/9)(x - color(red)(-10))#

#(y + color(red)(3)) = color(blue)(4/9)(x + color(red)(10))#

We can also substitute the slope we calculated and the values from the second point in the problem giving:

#(y - color(red)(1)) = color(blue)(4/9)(x - color(red)(-1))#

#(y - color(red)(1)) = color(blue)(4/9)(x + color(red)(1))#