# Question a65d7

Jan 18, 2018

$y = 5 x - 2$

#### Explanation:

We know that the linear equation is in the form of

$y = m x + b$, $m$ is the slope$,$b is the y-intercept

Given: $m = 5$, passes through $\left(3 , 13\right)$

$\therefore y = 5 x + b$

We also know that it passes through $\left(3 , 13\right)$, so we can plug that in for $x = 3 , y = 13$

$13 = 5 \cdot 3 + b$

$13 = 15 + b$

$b = - 2$

$\therefore y = 5 x - 2$

Jan 18, 2018

In point-slope form: $y - 13 = 5 \left(x - 3\right)$

In $y = m x + b$ form: $y = 5 x - 2$

#### Explanation:

We can use the point-slope formula to find the equation of the line

$y - {y}_{1} = m \left(x - {x}_{1}\right)$

Where $m$ is the slope and $\left({x}_{1} , {y}_{1}\right)$ is a point on the line

Given: $m = 5$ and $\left({x}_{1} , {y}_{1}\right) \to \left(3 , 13\right)$

$y - 13 = 5 \left(x - 3\right)$

This is the equation in point-slope form but this can be rewritten in $y = m x + b$ form

To do that, we'll solve the above equation for $y$

$y - 13 = 5 x - 15$

$y - 13 \textcolor{red}{+ 13} = 5 x - 15 \textcolor{red}{+ 13}$

$y - 0 = 5 x - 2$

$y = 5 x - 2$

The graph of the line is shown below:

graph{5x-2 [-10, 10, -5, 5]}