Question

How do you write an equation in slope-intercept form for a line that is parallel to the given line y = 1/3x + 5 and passes through the given point(0,-5)?

Answer 1

`y=1/3x-5`

Explanation:

As you might know, lines that are parallel have the same value at `x`, in this case `1/3`. This is because this represents the slope of the line, and same slope means parallel lines.
To get the full equation, there is a formula, but there's also a way if you don't know the formula. Let's do it without the formula first:

Without the formula
Let's write down what we know of our function at the moment:
`y=1/3x+c`
All we need to know is `c`. Since we know one of the points, we can just replace the `x` and `y` value and solve for `c`:
`-5=1/3*0+c`
`c=-5`
It's that easy! The equation is thus:
`y=1/3x-5`

With the formula
The formula to find the equation of a line through a given point and with a given slope is:

`y-y1=m(x-x1)`
where `y1` is the `y`-value of your point, `x1` the `x`-value and `m` the slope.
In this case, it will be:
`y-(-5)=1/3(x-0)`
`y+5=1/3x`
`y=1/3x-5`