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)(1) - color(blue)(8))/(color(red)(0) - color(blue)(-8)) = (color(red)(1) - color(blue)(8))/(color(red)(0) + color(blue)(8)) = -7/8#
We can now use the point-slope formula to write and equation for the line running between the two points in the problem. 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 first point in the problem gives:
#(y - color(red)(8)) = color(blue)(-7/8)(x - color(red)(-8))#
#(y - color(red)(8)) = color(blue)(-7/8)(x + color(red)(8))#
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)(-7/8)(x - color(red)(0))#
#(y - color(red)(1)) = color(blue)(-7/8)x#
We can also solve this equation for #y# to put it into 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)(1) = -7/8x#
#y - color(red)(1) + 1 = -7/8x + 1#
#y - 0 = -7/8x + 1#
#y = color(red)(-7/8)x + color(blue)(1)#
