# How do you write the equation of the line with slope m = 3 and including point (3, 5)?

Apr 6, 2016

The equation of a line is

$y = m x + c$

and $m$ is already given as $3$.

Therefore,

$y = 3 x + c$

where $c$ is found by substituting a point, which is given as $\left(3 , 5\right)$.

If $x = 3$ and $y = 5$ (as it says in the point given), then

$5 = 3 \cdot 3 + c$
$5 = 9 + c$
$c = - 4$

which we can substitute back in to give

$y = 3 x - 4$

Apr 6, 2016

y = 3x - 4

#### Explanation:

One form of the equation of a line is : y - b = m(x - a )

where m represents the gradient (slope ) and (a,b) a point on the line.

here m = 3 and (a,b) = (3,5)

substituting these values into the equation.

y - 5 = 3(x - 3) → y - 5 = 3x - 9 → y = 3x - 4