# How do you write an equation of a line given point (1,3) and m=-3/4?

Jan 9, 2017

Use the point-slope formula to write the equation of the line. See the full explanation below:

#### Explanation:

Use the point-slope formula to write the equation of the line.

The point-slope formula states: $\left(y - \textcolor{red}{{y}_{1}}\right) = \textcolor{b l u e}{m} \left(x - \textcolor{red}{{x}_{1}}\right)$

Where $\textcolor{b l u e}{m}$ is the slope and $\textcolor{red}{\left(\left({x}_{1} , {y}_{1}\right)\right)}$ is a point the line passes through.

Substituting the point and the slope from the problem gives the result:

$\left(y - \textcolor{red}{3}\right) = \textcolor{b l u e}{- \frac{3}{4}} \left(x - \textcolor{red}{1}\right)$

We can convert this to the more familiar slope=intercept form by solving for $y$:

$y - \textcolor{red}{3} = \textcolor{b l u e}{- \frac{3}{4}} x - \left(\textcolor{b l u e}{- \frac{3}{4}} \times \textcolor{red}{1}\right)$

$y - \textcolor{red}{3} = \textcolor{b l u e}{- \frac{3}{4}} x + \frac{3}{4}$

$y - \textcolor{red}{3} + 3 = \textcolor{b l u e}{- \frac{3}{4}} x + \frac{3}{4} + 3$

$y - 0 = \textcolor{b l u e}{- \frac{3}{4}} x + \frac{3}{4} + \left(\frac{4}{4} \times 3\right)$

$y = \textcolor{b l u e}{- \frac{3}{4}} x + \frac{3}{4} + \frac{12}{4}$

$y = - \frac{3}{4} x + \frac{15}{4}$