# Question d8011

Feb 2, 2017

$y = 3 x + 4 \text{ is correct}$

#### Explanation:

The equation of a line in color(blue)"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 $\textcolor{b l u e}{\text{ gradient formula}}$

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

The 2 points here are (0 ,4) and (1 ,7)

let $\left({x}_{1} , {y}_{1}\right) = \left(0 , 4\right) \text{ and } \left({x}_{2} , {y}_{2}\right) = \left(1 , 7\right)$

$\Rightarrow m = \frac{7 - 4}{1 - 0} = \frac{3}{1} = 3$

Either of the 2 points may be used as $\left({x}_{1} , {y}_{1}\right)$ as both lie on the line.

$\text{Using "m=3" and } \left({x}_{1} , {y}_{1}\right) = \left(1 , 7\right)$

Substitute these values into the equation.

$y - 7 = 3 \left(x - 1\right) \leftarrow \textcolor{red}{\text{ in point-slope form}}$

distributing and simplifying gives an alternative version of the equation.

$y - 7 = 3 x - 3 \Rightarrow y = 3 x - 3 + 7$

$\Rightarrow y = 3 x + 4 \leftarrow \textcolor{red}{\text{ in slope-intercept form}}$