How do you write the equation of a line in slope intercept form that is parallel to the line #y=1/3x+5# and passes through (-9, 5)?

1 Answer
EZ as pi
May 8, 2016

#y = -3x - 22#

Explanation:

If you have the slope of a line, #m# and one point, #(x_1, y_1)# the easiest way to find its equation is by using the formula: #y - y_1 = m(x - x_1)#

Let's find the slope first. If two lines are perpendicular, then the one slope is the negative reciprocal of the other.. ie #m_1 xxm_2 = -1#

The line we want to know about is perpendicular to a line with a slope of #1/3#, so the new slope is -3. We have the point #(-9,5)#

Substitute into #y - y_1 = m(x - x_1)# and simplify
#y - 5 = -3(x - (-9)) rArr y - 5 = -3(x + 9)#

#y = -3x - 27 + 5#

#y = -3x - 22#

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