How do you write an equation given points (5,7), (6,8)?

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Answer 1 · 2016-11-13T20:50:17

$y = x + 2$ $y=x+2$

First, find the slope of the line using slope formula:

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ $m=(y_2-y_1)/(x_2-x_1)$

Where $m$ $m$ is the slope

$(5, 7) \Rightarrow (x_{1}, y_{1})$ $(5,7)=>(x_1,y_1)$

$(6, 8) \Rightarrow (x_{2}, y_{2})$ $(6,8) => (x_2,y_2)$

$m = \frac{8 - 7}{6 - 5} = \frac{1}{1} = 1$ $m=(8-7)/(6-5)=1/1=1$

Next, pick a set of coordinate points and plug them into point slope form:

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

And the slope of $1$ $1$

If you use $(5, 7)$ $(5,7)$ :

$y - 7 = 1 (x - 5)$ $y-7=1(x-5)$

Distribute the one throughout the set of parenthesis

$y - 7 = x - 5$ $y-7=x-5$

Add $7$ $7$ on both sides of the equation

$y = x + 2$ $y=x+2$

If you were to use the other set of coordinate points, the equation should be the same:

If you use $(6, 8)$ $(6,8)$ :

$y - 8 = 1 (x - 6)$ $y-8=1(x-6)$

Distribute the one throughout the set of parenthesis

$y - 8 = x - 6$ $y-8=x-6$

Add $8$ $8$ on both sides of the equation

$y = x + 2$ $y=x+2$