Which equation represents the line that passes through the points (6,-3) and (-4,-9)?

Question

Eva Adamson · Accepted Answer

#(y + color(red)(9)) = color(blue)(3/5)(x + color(red)(4))#

or

#y = color(blue)(3/5)x - 33/5# Because we are given two points we can calculate the slope and then we can use the slope and either point and use the point-slope formula to find the equation for 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 two points from the problem gives: #m = (color(red)(-9) - color(blue)(-3))/(color(red)(-4) - color(blue)(6))# #m = (color(red)(-9) + color(blue)(3))/(color(red)(-4) - color(blue)(6))# #m = (-6)/(-10)# #m = 6/10 = 3/5# Now we have the slope and can use either point and the point-slope formula to find the equation 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 one of the points gives: #(y - color(red)(-9)) = color(blue)(3/5)(x - color(red)(-4))# #(y + color(red)(9)) = color(blue)(3/5)(x + color(red)(4))# We can convert to the more familiar slope-intercept form by solving for #y#: #y + color(red)(9) = color(blue)(3/5)x + (color(blue)(3/5) xx color(red)(4))# #y + color(red)(9) = color(blue)(3/5)x + 12/5# #y + color(red)(9) - 9 = color(blue)(3/5)x + 12/5 - 9# #y + 0 = color(blue)(3/5)x + 12/5 - (9 xx 5/5)# #y = color(blue)(3/5)x + 12/5 - 45/5# #y = color(blue)(3/5)x - 33/5#

Abigail Allen · Answer

undefined The equation representing the line that passes through the points (6,-3) and (-4,-9) is y = -0.6x - 0.6.