# What is the equation of the line with slope  m= -3  that passes through  (23,-23) ?

Dec 20, 2015

$y = - 3 x + 46$

#### Explanation:

The equation can be written in slope-intercept form, which is:

$y = m x + b$

where:
$y =$y-coordinate
$m =$slope
$x =$x-coordinate
$b =$y-intercept

Since we do not know the value of $b$ yet, this is going to be what we are trying to solve for. We can do this by substituting the point, $\left(23 , - 23\right)$, and the slope, $- 3$, into an equation. The only unknown value will be $b$:

$y = m x + b$
$- 23 = - 3 \left(23\right) + b$
$- 23 = - 69 + b$
$46 = b$

Now that you know all your values, rewrite the equation in slope-intercept form:

$y = - 3 x + 46$