Question

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

Answer 1

`y=-3x-2`

Explanation:

Given -

Slope of the line `-3`

Point `(-2, 4)`

Use the formula -

`mx+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`

`(-3)(-2) +C=4`

`6+c=4`

`c=4-6=-2`

`-3x-2=y`

The equation of the required line is

`y=-3x-2`

Answer 2

`y = -3x - 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 = mx + b`
where m is the slope of the line `((Delta y) / (Delta x))` 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 = (-3)*(-2) +b`
`4 = 6 + b`
`-2 = b`
The equation in slope intercept form is `y = -3x - 2`

Point Slope Form:

`(y-y_1) = m(x-x_1)`
Where m is the slope of the line `((Delta y) / (Delta x))`, `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`.
`(y - 4) = -3(x + 2)`

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.
`(y - 4) = -3(x + 2)`
`y - 4 = -3x - 6`
`y + 3x - 4 = - 6`

`y + 3x = - 2`