What is the equation in point-slope form of the line given (4, –4) and (9, –1)?

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Answer 1 · 2015-05-17T08:57:22

Firstly in this question we would need to find the "slope" or otherwise known as the gradient. we use the formula.

$m = \frac{Y 2 - Y 1}{X 2 - X 1}$ $m= (Y2 - Y1)/(X2-X1)$

so for this question we get.

$m = \frac{- 1 - (- 4)}{9 - 4}$ $m = (-1 - ( -4))/(9-4)$

$m = \frac{3}{5}$ $m = 3/5$

now we take a look at our equation for a straight line, which is.

$Y = m X + c$ $Y = mX + c$

we have now got a value for $m$ $m$ and we need to solve for a value for $c$ $c$ .

to do this, we use the $X$ $X$ and $Y$ $Y$ from either of the given points and put them into our formula. so we have:

$- 4 = (\frac{3}{5}) (4) + c$ $-4 = (3/5)(4) + c$
$- 4 = (\frac{12}{5}) + c$ $-4 = (12/5) + c$
$- 4 - (\frac{12}{5}) = c$ $-4 - (12/5) =c$

$c = - \frac{32}{5}$ $c = -32/5$

now all we need to do is insert our value for $c$ $c$ into our straight line equation. thus we end up with.

$Y = (\frac{3}{5}) X - (\frac{32}{5})$ $Y = (3/5)X - (32/5)$