# How do you write the equation of the line with (1, 7) and (2, 10)?

Mar 31, 2018

$y = 3 x + 4$

#### Explanation:

$\text{the equation of a line in "color(blue)"slope-intercept form}$ is.

•color(white)(x)y=mx+b

$\text{where m is the slope and b the y-intercept}$

$\text{to calculate m use the "color(blue)"gradient formula}$

•color(white)(x)m=(y_2-y_1)/(x_2-x_1)

$\text{let "(x_1,y_1)=(1,7)" and } \left({x}_{2} , {y}_{2}\right) = \left(2 , 10\right)$

$\Rightarrow m = \frac{10 - 7}{2 - 1} = \frac{3}{1} = 3$

$\Rightarrow y = 3 x + b \leftarrow \textcolor{b l u e}{\text{is the partial equation}}$

$\text{to find b substitute either of the 2 given points into}$
$\text{the partial equation}$

$\text{using "(1,7)" then}$

$7 = 3 + b \Rightarrow b = 7 - 3 = 4$

$\Rightarrow y = 3 x + 4 \leftarrow \textcolor{red}{\text{is the equation of line}}$