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))#
