Question

How do you write the equation of the line that passes through the point (6, -2) and has a slope of -2/3?

Answer 1

`y=-2/3x+2`

Explanation:

Given that we have the slope and a point on the graph we can use the point slope formula to find the equation of the line.

Point-Slope Formula: `y-y_1=m(x-x_1)`, where `m` is the slope of the line and `x_1` and `y_1` are x and y coordinates of a given point.

We can summarize the information already given:

`m=-2/3`

`x_1=6`

`y_1=-2`

Using this information, we can substitute these values onto the point-slope formula:

`y-(-2)=-2/3(x-(6))`

`y+2=-2/3(x-6)`

The equation above is the equation of the line in point-slope form. If we wanted to have the equation in `y=mx+b` form then we simply solve the equation above for `y`

`y+2=-2/3x+12/3`

`ycancel(+2-2)=-2/3x+12/3-2`

`y=-2/3x+12/3-2(3/3)`

`y=-2/3x+12/3-6/3`

`y=-2/3x+6/3`

`y=-2/3x+2`