How do you write an equation in slope intercept form given (1,-3) and (-2,-4)?

1 Answer
May 31, 2017

See a solution process below:

Explanation:

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)(-4) - color(blue)(-3))/(color(red)(-2) - color(blue)(1)) = (color(red)(-4) + color(blue)(3))/(color(red)(-2) - color(blue)(1)) = (-1)/-3 = 1/3#

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.

We can substitute the slope and the values for one of the points and solve for #b#:

#-3 = (color(red)(1/3) xx 1) + color(blue)(b)#

#-3 = 1/3 + color(blue)(b)#

#-color(red)(1/3) - 3 = -color(red)(1/3) + 1/3 + color(blue)(b)#

#-color(red)(1/3) - (3/3 xx 3) = 0 + color(blue)(b)#

#-color(red)(1/3) - 9/3 = color(blue)(b)#

#-10/3 = color(blue)(b)#

We can now substitute the slope and #b# value we calculated into the formula giving:

#y = color(red)(1/3)x + color(blue)(-10/3)#

#y = color(red)(1/3)x - color(blue)(10/3)#