What's the equation of a line that passes through (1,2) (3,5)?

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Answer 1 · 2015-06-26T23:13:13

In slope-intercept form, the equation of the line is:

$y = 3/2x + 1/2$

as derived below...

First let's determine the slope $m$ of the line.

If a line passes through two points $(x_1, y_1)$ and $(x_2, y_2)$ then its slope $m$ is given by the formula:

$m = (Delta y)/(Delta x) = (y_2 - y_1)/(x_2 - x_1)$

In our example, $(x_1, y_1) = (1, 2)$ and $(x_2, y_2) = (3, 5)$ , so

$m = (y_2 - y_1)/(x_2 - x_1) = (5 - 2)/(3 - 1) = 3/2$

In slope-intercept form, the line has the equation:

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

We know $m=3/2$ , but what about $c$ ?

If we substitute the values for $(x, y) = (1, 2)$ and $m = 3/2$ into the equation, we get:

$2 = (3/2)*1 + c = 3/2+c$

Subtract $3/2$ from both sides to get:

$c = 2 - 3/2 = 1/2$

So the equation of the line can be written:

$y = 3/2x + 1/2$