Question

What is the equation of a line passing through (-3, 7) and having a slope of ?

y = -5x + 22

y = 5x + 22

Answer 1

You missed the slope there.
But let's take a closer look to the slope formula:
\[m=\frac{ y_2 - y_1 }{ x_2 - x_1 }\]
So we know that the way to calculate the slope is the division between the change in y and the change in x.
Buw if we know the slope and one of the points that belong to that line then I must be able to find the equation of the line by making it have that structure, by that, let's multiply both sides by (x2 - x1) :
\[m( x_2 - x_1 ) = ( y_2 - y_1 )\]
So, this must mean that at least one of them must be generic, in order to find the line that belong to any point (x,y) and a known point (a,b) I'd just have to replace:
\[m(x-a)=(y-b)\]
Doing the distributive:
\[mx-ma=y-b\]
\[mx-y+b-ma=0\]
We can see it has the form "Ax+By+C=0" wich corresponds to a line, giving me the certainty that this is a valid formula to find the line knowing a point an it's slope.
We conclude that the formula is:
\[(y- y_o)=m(x- x_o )\]
Where "m" is the slope and "xo" and "yo" are the coordinates of a known point.