How do you write an equation in point slope and slope intercept form given (4,5) & (7,9)?

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Answer 1 · 2017-05-04T17:03:03

Point-slope form: #y - 5 = 4/3 (x - 4)#

Slope intercept form: #y = 4/3x -1/3#

First find the slope #= m = (Delta y)/(Delta x) = (y_2-y_1)/(x_2 - x_1)#:

#m = (9-5)/(7-4) = 4/3#

Point-slope form #y - y_1 = m (x - x_1)#:

#y - 5 = 4/3 (x - 4)#

To find the slope intercept form #y = mx + b#:

Use the point-slope form and distribute: #y - 5 = 4/3x - 4/3 *4/1#

Simplify:

#y - 5 = 4/3x -16/3#

# y = 4/3x - 16/3 +5/1#

#y = 4/3x - 16/3 + 15/3#

#y = 4/3x -1/3#

Use slope and one point to find the #y#-intercept #b#:

#y = 4/3x + b#

#9 = 4/3 * 7/1 + b#

#9/1 = 28/3 + b#

#27/3 - 28/3 = b#

#b = -1/3#

#y = 4/3x - 1/3#