How do you write an equation in standard form given a line that passes through (-5, 9) (3, -2)?

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Answer 1 · 2018-06-26T00:19:04

#8y + 11y = 17#

Given: #(-5, 9), (3, -2)#

Find the slope of the line: #m = (y_2 - y_1)/(x_2 - x_1) " or " m = (y_1 - y_2)/(x_1 - x_2)#

#m = (9 - -2)/(-5 - 3) = 11/-8 = -11/8#

Use #y = mx + b# and one of the points to find #b#, the #y#-intercept:

#9 = -11/8 * -5/1 + b#

#9 = 55/8 + b#

#9/1 * 8/8 - 55/8 = b#

#b = (72 - 55)/8 = 17/8#

#y = -11/8 x + 17/8#

Standard form: #Ax + By = C#

Multiply the whole equation by #8: " "8y = -11x + 17#

#8y + 11y = 17#