# How do you find an equation of the line with slope 3 that contains the point (4, 1)?

Apr 8, 2015
• The Point-Slope form of the Equation of a Straight Line is:

$\left(y - k\right) = m \cdot \left(x - h\right)$
$m$ is the Slope of the Line

$\left(h , k\right)$ are the co-ordinates of any point on that Line.

• Here, we have been given the coordinates $\left(h , k\right)$ of 1 point on that line as $\left(4 , 1\right)$
And the Slope $m$ is given as $3$

Substituting the values of h, k and m in the Point-Slope form, we get

$\left(y - 1\right) = 3 \cdot \left(x - 4\right)$
The above will be the Equation of the Line in Point-Slope form.

• If we need it in the Slope Intercept Form, we need to follow these steps:

$\left(y - 1\right) = 3 x - 12$

$y = 3 x - 12 + 1$

$y = 3 x - 11$

We get the equation of the line as :

color(green)( y=3x - 11

The graph will look like this:

graph{ y=3x - 11 [-10, 10, -5, 5]}