First we need to determine the slope from the two points provided in the problem. 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 value from the points and calculating gives:
#m = (color(red)(0) - color(blue)(-2))/(color(red)(8) - color(blue)(0))#
#m = (color(red)(0) + color(blue)(2))/(color(red)(8) - color(blue)(0))#
#m = 2/8 = 1/4#
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 value from the y-intercept given in the problem results in:
#y = color(red)(1/4)x + color(blue)(-2)#
#y = color(red)(1/4)x - color(blue)(2)#
