Question

What is the equation of the line with slope `m= -3/7` that passes through `(17/13,14/7)`?

Answer 1

`y = -3/7x + \frac{233}{91}`

Explanation:

When you know a given point `(x_0,y_0)` and the slope `m`, the equation of a line is

`y-y_0 = m(x-x_0)`

In your case, `(x_0,y_0) = (\frac{17}{13}, \frac{14}{7}) = (\frac{17}{13},2)` and `m=-3/7`.

Let's plug these values in the formula:

`y-2 = -3/7(x-\frac{17}{13})`

Although this already is the equation of the line, you may want to write in the slope-intercept form, for example. Expanding the right hand side, we have

`y-2 = -3/7x+\frac{51}{91}`

add `2` to both sides to get

`y = -3/7x + \frac{233}{91}`