# Which line has a slope of 7 and goes through the point (3,6)?

## Which line has a slope of 7 and goes through the point (3,6)?

Apr 7, 2018

$y - 6 = 7 \left(x - 3\right) \leftarrow$ Point-Slope form

$y = 7 x - 15 \leftarrow$ Slope-Intercept form

#### Explanation:

We'll make use of the point-slope formula which is:

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

In this case, $m$ is the slope which is $7$, so $m = 7$

Also, $\left({x}_{1} , {y}_{1}\right)$ is a point on the line and we are given the point $\left(3 , 6\right)$. So $\left({x}_{1} , {y}_{1}\right) = \left(3 , 6\right)$

Substituting this into the point slope formula gives...

$y - 6 = 7 \left(x - 3\right)$

This is a valid equation of the line in point-slope form. However, we can rewrite this is a more familiar form: slope-intercept form $\left(y = m x + b\right)$

To do this, all we do is solve for $y$

$y - 6 = 7 \left(x - 3\right)$

$y - 6 = 7 x - 21$

$y = 7 x - 21 + 6$

$y = 7 x - 15$

Use the following link to see both variations of the equations of the line passing thorugh the point $\left(3 , 6\right)$

https://www.desmos.com/calculator/8iwichloir