Question

A line passes through point (2, 5) and has a slope of 3. Write an equation in Ax +By=C form for this line. Use integers for A, B, and C. ​

Answer 1

Answer:

$3\, x + (-1)\, y = 1$.

Step-by-step explanation:

Both the slope of this line and the coordinates of a point on this line are given. Therefore, start by finding the point-slope equation of this line: if the slope of a line in a plane is $m$, and this line goes through a point at $(x_{0},\, y_{0})$, the point-slope equation of this line will be $(y - y_{0}) = m\, (x - x_{0})$.

The slope of the line in this question is $m = 3$. It is given that this line goes through the point $(2,\, 5)$, where $x_{0} = 2$ and $y_{0} = 5$. Substitute in these values to find the point-slope equation of this line:

$(y - y_{0}) = m\, (x - x_{0})$.

$(y - 5) = 3\, (x - 2)$.

Rewrite this point-slope equation in the requested format:

$y - 5 = 3\, x - 6$.

$3\, x - 6 = y - 5$.

$3\, x = y + 1$.

$3\, x - y = 1$.

$3\, x + (-1)\, y = 1$.