How do you write the equation in slope intercept form given (2,7) and (-4,1)?

1 Answer
smendyka
Apr 22, 2017

See the entire solution process below:

Explanation:

First, 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)(1) - color(blue)(7))/(color(red)(-4) - color(blue)(2)) = (-6)/-6 = 1#

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 we calculated and one of the points from the problem for #x# and #y# and then solve for #b#:

#7 = (color(red)(1) * 2) + color(blue)(b)#

#7 = 2 + color(blue)(b)#

#-color(red)(2) + 7 = -color(red)(2) + 2 + color(blue)(b)#

#5 = 0 + color(blue)(b)#

#5 = color(blue)(b)#

We can now substitute the slope and y-intercept we calculated into the formula:

#y = color(red)(1)x + color(blue)(5)#

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