Question

How do you write an equation with slope of 5/3 and contains the point (-6, -2)?

Answer 1

`y = 5/3x+8`

Explanation:

To do this, we use a linear equation called point slope form. This is basically another way of writing a linear equation, like `y = mx+b`. Point slope form is as follows: `y-y_1 = m(x-x_1)`. I won't go into the specifics of what this equation is or how it's derived, but I encourage you to do so. In this equation, `y_1` and `x_1` are points on the line `y` and `m` is the slope.

Here, we already have the elements: points on the line, and the slope. To solve, we just substitute these values into the equation and simplify:
`y-(-2) = (5/3)(x-(-6))`; `x_1 = -6`, `y_1 = -2`, `m = 5/3`
`y+2 = 5/3(x+6)`
`y+2 = 5/3x+10`
`y = 5/3x+10-2`
`y = 5/3x+8`
And there you have it - the equation of the line with slope 5/3 and passing through the point (-6,-2).