The x-intercept of -2 can be written as #(-2, 0)#
The y-intercept of 1 can be written as #(0, 1)#
Knowing two points we can find the slope. 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)(1) - color(blue)(0))/(color(red)(0) - color(blue)(-2)) = (color(red)(1) - color(blue)(0))/(color(red)(0) + color(blue)(2)) = 1/2#
We can now use the point-slope formula to find equations for the line. 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 values from the second point gives:
#(y - color(red)(1)) = color(blue)(1/2)(x - color(red)(0))#
#y - color(red)(1) = color(blue)(1/2)x#
We can also substitute the slope we calculated and the values from the first point giving:
#(y - color(red)(0)) = color(blue)(1/2)(x - color(red)(-2))#
#(y - color(red)(0)) = color(blue)(1/2)(x + color(red)(2))#
We can solve this for #y# to put it into the slope-intercept form. 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.
#y - color(red)(0) = (color(blue)(1/2) xx x) + (color(blue)(1/2) xx color(red)(2))#
#y - color(red)(0) = 1/2x + 1#
#y = color(red)(1/2)x + color(blue)(1)#
