How do you write an equation in standard form given that the line has slope m=5 through (-6,9)?

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Answer 1 · 2015-05-26T22:30:41

If a line has slope #m# and passes through a point #(x_0, y_0)# then it can be expressed in point-slope form by the equation:

#y - y_0 = m(x - x_0)#

So in your example, we would write:

#y - 9 = 5(x - (-6))#

It can also be expressed in point-intercept form - that is in the form:

#y = mx + c#

We know #m=5# and an example point #(-6, 9)# that will satisfy this equation, so we have:

#9 = 5(-6)+c = -30 + c#

Add #30# to both sides to get #c = 39#. So our line can be written in point-intercept form as:

#y = 5x + 39#