First, we need to determine the slope of the line. 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)(3) - color(blue)(0))/(color(red)(-4) - color(blue)(0)) = -3/4#
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 second point gives:
#(y - color(red)(3)) = color(blue)(-3/4)(x - color(red)(-4))#
#(y - color(red)(3)) = color(blue)(-3/4)(x + color(red)(4))#
We can also substitute the slope we calculated and the first point giving:
#(y - color(red)(0)) = color(blue)(-3/4)(x - color(red)(0))#
