# How do you find a standard form equation for the line with (1,5), m=0?

Jun 3, 2016

$y = 5$

#### Explanation:

m is the gradient which is the amount of up or down for 1 along.

However, m=0 which means that there is no up or down. Consequently the line is horizontal (parallel to x-axis)

This horizontal line passes through $\left(x , y\right) \to \left(1 , 5\right)$

So this horizontal line passes through $y = 5$

This is the equation of the line.
,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Using algebra}}$

Standard form equation is $y = m x + c$

Given that $m = 0$ and the line passes through the point (1,5) we have:

color(brown)(y=mx+c)color(blue)(" "->" "5=(0xx1)+c

Thus $c = 5$

So $y = \left(0 \times x\right) + 5$

$y = 5$