How do you write the equation of a line given (2,4) (-4,-5)?

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Answer 1 · 2017-05-20T11:37:05

We write the equation in 'point-slope' form, so we need to find the y-intercept and the gradient (slope).

The equation of the line is $y=3/2x+1$

We will find the equation of the line in 'point-slope' form:

$y=mx+c$ where $m$ is the gradient and $c$ is the y-intercept.

First we need to find the gradient (slope) of the line:

$m=(y_2-y_1)/(x_2-x_1) = (-5-4)/(-4-2) = (-9)/(-6) = 3/2$

Now we need to find the y-intercept, $c$ . (sometimes people call it 'b')

We can choose either of the points we are given to substitute into the equation. Let's choose $(2,4)$ .

$y=mx+c$

$4=3/2(2)+c$

$c=1$

Over all, then, the equation of the line is $y=3/2x+1$