How do you write a linear function equation that passes through points (-2,5) and (-4,7)?

Nov 26, 2016

$y = - x + 3$

Explanation:

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

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y - {y}_{1} = m \left(x - {x}_{1}\right)} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
where m represents the slope and $\left({x}_{1} , {y}_{1}\right) \text{ a point on the line}$

To calculate m, use the $\textcolor{b l u e}{\text{gradient formula}}$

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder }} \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
where $\left({x}_{1} , {y}_{1}\right) , \left({x}_{2} , {y}_{2}\right) \text{ are 2 points on the line}$

The 2 points here are (-2 ,5) and (-4 ,7)

$\Rightarrow m = \frac{7 - 5}{- 4 - \left(- 2\right)} = \frac{2}{- 2} = - 1$

Use either of the 2 given points for $\left({x}_{1} , {y}_{1}\right)$

substitute m = - 1 and (-2 ,5) into the equation.

$y - 5 = - 1 \left(x + 2\right) \Rightarrow y - 5 = - x - 2$

which simplifies to.

$y = - x + 3$