Question

What is the equation of the line with slope `m= -43/49` that passes through `(19/7, 33/21)`?

Answer 1

`y = (-43/49)x + (1356/343)`

Explanation:

To find the equation of a line given the slope and a point of intersection, use the point-slope formula.

The point slope formula is written as: `y-y_1 = m(x-x_1)`. Substitute the given information into the formula by setting `y_1 = 33/21, x_1 = 19/7, and m = -43/49`.

You should get: `y - (33/21) = (-43/49)(x-(19/7))`.

Distribute the slope into `(x - 19/7)` and get: `y - (33/21) = (-43/49)x + (817/343)`.

Now solve for `y` by adding `33/21` to both sides to isolate the variable.

`y=-43/49x+817/343+33/21`

`y=-43/49x+817/343(3/3)+33/21(49/49)`

`y=-43/49x+2451/1029+1617/1029`

`y=-43/49x+4068/1029`

`y=-43/49x+(3/3)(1356/343)`

You should end up with `y = (-43/49)x + (1356/343)`.