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 $y$ $y$ − $1$ $1$ = $m$ $m$ ∗ $(x + 2)$ $(x + 2)$ , where $m$ $m$ is $\frac{5}{7}$ $5/7$ .

First, start with your point-slope formula:

$y$ $y$ − $y_{1}$ $y_1$ = $m$ $m$ ∗ $(x - x_{1})$ $(x−x_1)$

Label your ordered pairs:

$(- 2, 1)$ $(-2, 1)$ = $(X_{1}, Y_{1})$ $(X_1, Y_1)$
$(5, 6)$ $(5, 6)$ = $(X_{2}, Y_{2})$ $(X_2, Y_2)$

$y$ $y$ − $1$ $1$ = $m$ $m$ ∗ $(x - - 2)$ $(x−-2)$

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

$y$ $y$ - $1$ $1$ = $m$ $m$ ∗ $(x + 2)$ $(x+2)$

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

$\frac{Y_{2} - Y_{1}}{X_{2} - X_{1}}$ $(Y_2 - Y_1)/(X_2 - X_1)$ = $m$ $m$ , where $m$ $m$ is the slope.

Now, label your ordered pairs as $X_{1}$ $X_1$ , $X_{2}$ $X_2$ , $Y_{1}$ $Y_1$ , and $Y_{2}$ $Y_2$ :

$(- 2, 1)$ $(-2, 1)$ = $(X_{1}, Y_{1})$ $(X_1, Y_1)$
$(5, 6)$ $(5, 6)$ = $(X_{2}, Y_{2})$ $(X_2, Y_2)$

Now, plug your data into the formula:

$\frac{6 - 1}{5 - - 2}$ $(6 - 1)/(5 - - 2)$ = $m$ $m$

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

$\frac{6 - 1}{5 + 2}$ $(6 - 1)/(5+2)$ = $m$ $m$

Simplify.

$\frac{5}{7}$ $5/7$ = $m$ $m$

Therefore, $m$ $m$ = $\frac{5}{7}$ $5/7$ .