What is the point-slope form of the line that passes through (-2,1) and (5,6)?

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Answer 1 · 2018-05-01T18:51:09

The point-slope formula is $y$ − $1$ = $m$ ∗ $(x + 2)$ , where $m$ is $5/7$ .

First, start with your point-slope formula:

$y$ − $y_1$ = $m$ ∗ $(x−x_1)$

Label your ordered pairs:

$(-2, 1)$ = $(X_1, Y_1)$
$(5, 6)$ = $(X_2, Y_2)$

$y$ − $1$ = $m$ ∗ $(x−-2)$

Two negatives make a positive, so, this is your equation:

$y$ - $1$ = $m$ ∗ $(x+2)$

Here's how to solve for $m$ to plug-it into your point-slope formula:

$(Y_2 - Y_1)/(X_2 - X_1)$ = $m$ , where $m$ is the slope.

Now, label your ordered pairs as $X_1$ , $X_2$ , $Y_1$ , and $Y_2$ :

$(-2, 1)$ = $(X_1, Y_1)$
$(5, 6)$ = $(X_2, Y_2)$

Now, plug your data into the formula:

$(6 - 1)/(5 - - 2)$ = $m$

5 - - 2 becomes 5 + 2 because two negatives create a positive. Now, the equation is:

$(6 - 1)/(5+2)$ = $m$

Simplify.

$5/7$ = $m$

Therefore, $m$ = $5/7$ .