We can use the point-slope formula to write an equation for this 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 and values from the point in the problem gives:
#(y - color(red)(-15/24)) = color(blue)(-8/3)(x - color(red)(-17/15))#
#(y + color(red)(15/24)) = color(blue)(-8/3)(x + color(red)(17/15))#
We can also solve this equation for #y# to transform it to 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)(15/24) = (color(blue)(-8/3) xx x) + (color(blue)(-8/3) xx color(red)(17/15))#
#y + color(red)(15/24) = -8/3x - 136/45#
#y + color(red)(15/24) - 15/247 = -8/3x - 136/45 - 15/24#
#y + 0 = -8/3x - (24/24 xx 136/45) - (45/45 xx 15/24)#
#y = -8/3x - (3264/1080) - (675/1080)#
#y = -8/3x - 3939/1080#
#y = -8/3x - (3 xx 1313)/(3 xx 360)#
#y = -8/3x - (color(red)(cancel(color(black)(3))) xx 1313)/(color(red)(cancel(color(black)(3))) xx 360)#
#y = -8/3x - 1313/360#
