#x#-intercept of #-3# is the same as #(-3, 0)#
#y#-intercept of #2# is the same as #(0, 2)#
First, we can find 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)(2) - color(blue)(0))/(color(red)(0) - color(blue)(-3)) = (color(red)(2) - color(blue)(0))/(color(red)(0) + color(blue)(3)) = 2/3#
We can now use the slope-intercept formula to write and equation for the line. The slope-intercept form of a linear equation is: #y = color(red)(m)x + color(blue)(b)#
Where #color(red)(m)# is the slope and #color(blue)(b)# is the y-intercept value.
Substituting the slope we calculated and the #y#-intercept given in the problem gives:
#y = color(red)(2/3)x + color(blue)(2)#