Question

Question #273da

Answer 1

`-7x + 12y = 21`

Explanation:

Assuming the question is to find the equation of the line passing through those two points:

Step 1: Find the slope of the line
The slope `m` of a line passing through the points `(x_1, y_1)` and `(x_2, y_2)` is given by

`m = (y_2-y_1)/(x_2-x_1)`

Substituting the given points in, we get

`m = (7 - 0)/(9 - (-3)) = 7/12`

Step 2: Write the equation of the line in point-slope form
The point-slope form of a line with slope `m` and passing through the point `(x_1, y_1)` is

`y - y_1 = m(x-x_1)`

Substituting one of the given points and our slope, we get

`y - 0 = 7/12(x - (-3))`

`=> y = 7/12(x+3)`

Step 3: Convert the equation into standard form
The standard form of a line is `Ax + By = C` where, if possible, `A,B,` and `C` are integers without a common factor. We perform algebraic manipulations on the above equation until it matches this form.

`y = 7/12(x+3)`

`=> y = 7/12x + 7/4`

`=> -7/12x + y = 7/4`

`:.-7x + 12y = 21`