# What is the equation of the line that has a slope of 4 and goes through (1,9)?

Oct 22, 2016

$y = 4 x + 13$

#### Explanation:

When you are given the slope and a set of points, you use point slope form, which is:

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

Where $m$ is the slope, ${y}_{1}$ is the $y$ in the set of points, and ${x}_{1}$ is the $x$ in the set of points

So, plug in your numbers

$y - 9 = 4 \left(x - 1\right)$

Distribute the $4$ throughout the set of parenthesis on the right

$y - 9 = 4 x - 4$

Begin to isolate y by adding $9$ on both sides of the equation

$y = 4 x + 5$

Oct 22, 2016

The equation in point-slope form is $y - 9 = 4 \left(x - 1\right)$.

#### Explanation:

Use the point-slope form of a linear equation, which is
$y - {y}_{1} = m \left(x - {x}_{1}\right)$
where m is the slope of the line and $\left({x}_{1} , {y}_{1}\right)$ is a point on the line.

$y - 9 = 4 \left(x - 1\right)$

If the answer needs to be in slope-intercept form, solve the equation for $y$:

$y - 9 = 4 \left(x - 1\right)$
$y - 9 = 4 x - 4$
$y - 9 + 9 = 4 x - 4 + 9$
$y = 4 x + 5$

If the answer needs to be in standard form, continue using inverse operations to take the equation from slope-intercept form to standard form.

$y = 4 x + 5$
$- 4 x + y = 4 x - 4 x + 5$
$- 4 x + y = 5$
$- 1 \left(- 4 x + y = 5\right)$
$4 x - y = - 5$