What is an equation for a line going through the points: #(-17, 10)# and #(9, 0)#?

Question

Isaiah Anthony · Accepted Answer

See the entire solution process below:

First, we need to determine 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)(0) - color(blue)(10))/(color(red)(9) - color(blue)(-17)) = (color(red)(0) - color(blue)(10))/(color(red)(9) + color(blue)(17)) = -10/26 = -5/13# Now, we can use the point-slope formula to find an 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 the first point from the problem gives: #(y - color(red)(10)) = color(blue)(-5/13)(x - color(red)(-17))# #(y - color(red)(10)) = color(blue)(-5/13)(x + color(red)(17))# Or, we can substitute the slope we calculated and the second point from the problem giving: #(y - color(red)(0)) = color(blue)(-5/13)(x - color(red)(9))# #y = color(blue)(-5/13)(x - color(red)(9))# Or, we can expand this to put the equation in 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(blue)(-5/13) xx x) - (color(blue)(-5/13) xx color(red)(9))# #y = color(red)(-5/13)x + color(blue)(45/13)# Three possible solutions are: #(y - color(red)(10)) = color(blue)(-5/13)(x + color(red)(17))# #y = color(blue)(-5/13)(x - color(red)(9))# #y = color(red)(-5/13)x + color(blue)(45/13)#

Jace Anderson · Answer

undefined The equation for a line going through the points (-17, 10) and (9, 0) is y = -0.5x + 0.5.