How do you write a line with slope = 3; (1, 5) ?

Apr 21, 2017

See the entire solution process below:

Explanation:

We can use the point-slope formula to write an equation with the slope in the problem and going through the point in the problem. 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 slope and values from the point in the problem gives:

$\left(y - \textcolor{red}{5}\right) = \textcolor{b l u e}{3} \left(x - \textcolor{red}{1}\right)$

We can also find the equation in slope-intercept form. The slope-intercept form of a linear equation is: $y = \textcolor{red}{m} x + \textcolor{b l u e}{b}$

Where $\textcolor{red}{m}$ is the slope and $\textcolor{b l u e}{b}$ is the y-intercept value.

Substituting the slope and the value from the point in the problem and solving for $b$ gives:

$5 = \left(\textcolor{red}{3} \cdot 1\right) + \textcolor{b l u e}{b}$

$5 = 3 + \textcolor{b l u e}{b}$

$- \textcolor{red}{3} + 5 = - \textcolor{red}{3} + 3 + \textcolor{b l u e}{b}$

$2 = 0 + \textcolor{b l u e}{b}$

$2 = \textcolor{b l u e}{b}$

Substituting this $2$ for $b$ and the slope from the problem into the formula gives the equation for the line as:

$y = \textcolor{red}{3} x + \textcolor{b l u e}{2}$