# How do you write the equation of the line through (4, 7) and (-2, 1) in point-slope form?

Jul 6, 2016

$y = x + 3.$

#### Explanation:

Eqn. of a line passing thro. pts. $\left({x}_{1} , {y}_{1}\right) \mathmr{and} \left({x}_{2} , {y}_{2}\right)$ is $: \frac{y - {y}_{1}}{x - {x}_{1}} = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$.

This may not turn out to be in the Point-Slope Form [in the Usual Notation ] $: y = m x + c \ldots \ldots \ldots \ldots \ldots \ldots \ldots \left(I\right)$, but we can convert it in that form.

Instead, let us start with assuming the reqd. eqn. in the desired form, i.e., $\left(I\right)$.

Now, $\left(4 , 7\right) \in \left[y = m x + c\right] \Rightarrow 7 = 4 m + c \ldots \ldots . . \left(1\right)$, & $\left(- 2 , 1\right) \in \left[y = m x + c\right] \Rightarrow 1 = - 2 m + c \ldots \ldots \ldots \ldots \left(2\right)$

$\left(1\right) - \left(2\right) \Rightarrow 6 = 6 m \Rightarrow m = 1$ & [$m$, together with $\left(1\right)$] $\Rightarrow c = 3.$

finally, we have the eqn. $: y = x + 3.$

Hope, you enjoyed it, as I do!