Question

a line passes through point (2, 1) and has a slope of -4. write an equation in ax + by = c form for this line. use integers for a, b, and c.

Explanation:

Step1: Use point-slope form

The point-slope formula is $y - y_1 = m(x - x_1)$, where $(x_1,y_1)=(2,1)$ and $m=-4$.
$y - 1 = -4(x - 2)$

Step2: Expand the right-hand side

Distribute the slope to the terms in parentheses.
$y - 1 = -4x + 8$

Step3: Rearrange to $Ax+By=C$ form

Move all terms to one side to get integer coefficients.
$4x + y = 8 + 1$

Step4: Simplify the constant term

Calculate the sum on the right-hand side.
$4x + y = 9$

Answer:

$4x + y = 9$