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:

$y = 5x + 39$