How do you write an equation of the line in slope-intercept form given the slope and a point that lies on the line: m=-1/13 and (-7,5)?

Question

Eva Adamson · Accepted Answer

The slope-intercept for of the equation meeting the requirements of this problem is:

#y = color(blue)(-1/13)x + color(red)(58/13)# To first identify the equation we can use the point-slope formula and then translate into the slope-intercept form. 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. We have been given the slope #color(blue)(m = -1/13)# We have been given a point on the line #color(red)(((-7, 5)))# Substituting gives: #(y - color(red)(5)) = color(blue)(-1/13)(x - color(red)(-7))# #(y - color(red)(5)) = color(blue)(-1/13)(x + color(red)(7))# The slope-intercept form of a linear equation is: #y = color(blue)(m)x + color(red)(b)# Where #color(blue)(m)# is the slope and #color(red)(b# is the y-intercept value. We can solve for #y# to put our equation into this form: #(y - color(red)(5)) = color(blue)(-1/13)(x + color(red)(7))# #(y - color(red)(5)) = color(blue)(-1/13)x + (color(blue)(-1/13) * color(red)(7)))# #y - color(red)(5) = color(blue)(-1/13)x + (color(blue)(-7/13))# #y - 5 = color(blue)(-1/13)x - 7/13# #y - 5 + color(red)(5) = color(blue)(-1/13)x - 7/13 + color(red)(5)# #y - 0 = color(blue)(-1/13)x - 7/13 + (color(red)(5) * 13/13)# #y = color(blue)(-1/13)x - 7/13 + color(red)(65/13)# #y = color(blue)(-1/13)x + color(red)(58/13)#

Eli Assouline · Answer

undefined The equation of the line in slope-intercept form given the slope $ m = -\frac{1}{13} $ and a point $ (-7, 5) $ is $ y = -\frac{1}{13}x + \frac{54}{13} $.