# How do you write an equation of a line with slope of -3 and passing through (-2,4)?

Mar 9, 2018

$y = - 3 x - 2$

#### Explanation:

Given -

Slope of the line $- 3$

Point $\left(- 2 , 4\right)$

Use the formula -

$m x + c = y$

Where -

$m$ slope of the line
$x , y$ x and y coordinates, through which the line passes

in our case -

$m = - 3$
$x = - 2$
$y = 4$

$\left(- 3\right) \left(- 2\right) + C = 4$

$6 + c = 4$

$c = 4 - 6 = - 2$

$- 3 x - 2 = y$

The equation of the required line is

$y = - 3 x - 2$

Mar 9, 2018

$y = - 3 x - 2$

#### Explanation:

There are three ways to write the equation of a line: slope intercept form, point slope form, and standard (general) form.

Slope Intercept Form:

$y = m x + b$
where m is the slope of the line $\left(\frac{\Delta y}{\Delta x}\right)$ and b is the y-intercept.
For a line with slope -3 and point (-2,4), plug -3 in for m, -2 for x, 4 for y, and solve for b.
$4 = \left(- 3\right) \cdot \left(- 2\right) + b$
$4 = 6 + b$
$- 2 = b$
The equation in slope intercept form is $y = - 3 x - 2$

Point Slope Form:

$\left(y - {y}_{1}\right) = m \left(x - {x}_{1}\right)$
Where m is the slope of the line $\left(\frac{\Delta y}{\Delta x}\right)$, ${y}_{1}$ is the y coordinate of a point, and ${x}_{1}$ is the x coordinate of a point.

For a line with slope -3 and point (-2,4), plug -3 in for m, -2 for ${x}_{1}$, 4 for ${y}_{1}$.
$\left(y - 4\right) = - 3 \left(x + 2\right)$

Standard Form:

Ax + By = C

Where A, B, and C are integers. To write an equation in standard form, rewrite the equation in point slope form so that it fits the formula for standard form.
$\left(y - 4\right) = - 3 \left(x + 2\right)$
$y - 4 = - 3 x - 6$
$y + 3 x - 4 = - 6$

$y + 3 x = - 2$