How do you write an equation in slope intercept form given ( 2,-5), Slope -7/2?

Jul 11, 2016

$y = - \frac{7}{2} x + 2$

Explanation:

The equation of a line in $\textcolor{b l u e}{\text{slope-intercept form}}$ is

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{y = m x + b} \textcolor{w h i t e}{\frac{a}{a}} |}}}$
where m represents the slope and b, the y-intercept.

Here we are given the slope and require to find b.

We can write a partial equation : $y = - \frac{7}{2} x + b$

To calculate b, substitute the given point (2 ,-5) into the partial equation.

x = 2 , y = -5 : $- \frac{7}{\cancel{2}} \times \cancel{2} + b = - 5$

$\Rightarrow - 7 + b = - 5 \Rightarrow b = - 5 + 7 = 2$

$\Rightarrow y = - \frac{7}{2} x + 2 \text{ is equation in slope-intercept form}$