# How do you write the equation of a line that passes through (1,1) and has slope 1/4?

Apr 1, 2015

y-1= $\frac{1}{4}$ (x-1)

Apr 7, 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 $\left(1 , 1\right)$
And the Slope $m$ is given as $\frac{1}{4}$

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

$\left(y - 1\right) = \left(\frac{1}{4}\right) \cdot \left(x - 1\right)$
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:

Multiplying both sides with 4, we get:

$4 \cdot \left(y - 1\right) = x - 1$

$4 y - 4 = x - 1$

$4 y = x - 1 + 4$

$4 y = x + 3$

We get the equation of the line as :
$y = \left(\frac{1}{4}\right) \cdot x + \frac{3}{4}$

The graph will look like this:

graph{y=(1/4)*x+3/4 [-10, 10, -5, 5]}