# How do you write an equation of a line with slope of 3 and contains the point (4, 9)?

Mar 22, 2018

$y = 3 x - 3$

#### Explanation:

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

•color(white)(x)y=mx+b

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

$\text{here } m = 3$

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

$\text{to find b substitute "(4,9)" into the partial equation}$

$9 = 12 + b \Rightarrow b = 9 - 12 = - 3$

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

Mar 22, 2018

$y = 3 x - 3$

#### Explanation:

You can use the equation of a line in point-slope form:
$y - {y}_{1} = m \left(x - {x}_{1}\right)$

Make the following substitutions:
${x}_{1} = 4$ (the x-coordinate of the point)
${y}_{1} = 9$ (the y-coordinate of the same point)
$m = 3$ (the slope of the line)

That will give you:
$y - 9 = 3 \left(x - 4\right)$

Then simplify:
$y - 9 = 3 \left(x - 4\right)$
$y - 9 = 3 x - 12$
$y = 3 x - 3$