# How do you write the equation in point slope form given (-1,4) slope m=5/4?

Sep 25, 2016

$y = \frac{5}{4} x + 2 \frac{1}{4}$

#### Explanation:

Point-slope form is $y = m x + c$

You have been given the slope $\left(m\right)$ and a point $\left(x , y\right)$.

Substitute these values into $y = m x + c$ and solve to find a value for $c$.

$4 = \frac{5}{4} \left(- 1\right) + c$
$4 = - \frac{5}{4} + c$

$4 + \frac{5}{4} = c \text{ } \leftarrow \frac{5}{4} = 1 \frac{1}{4}$

$c = 2 \frac{1}{4}$

$y = \frac{5}{4} x + 2 \frac{1}{7} \text{ } \leftarrow$ the required equation
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There is also a formula which applies to this scenario directly, where you have the slope and a point.

$y - {y}_{1} = m \left(x - {x}_{1}\right)$

$y \textcolor{b l u e}{- 4} = \frac{5}{4} \left(x - \left(- 1\right)\right)$

$y = \frac{5}{4} x + \frac{5}{4} \textcolor{b l u e}{+ 4}$

$y = \frac{5}{4} x + 2 \frac{1}{4}$