Question

a line passes through point (-8, -7) and has a slope of \\(\frac{3}{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 $(x_1,y_1)=(-8,-7)$ and $m=\frac{3}{4}$.
$y - (-7) = \frac{3}{4}(x - (-8))$
Simplify to: $y + 7 = \frac{3}{4}(x + 8)$

Step2: Eliminate the fraction

Multiply all terms by 4 to clear the denominator.
$4(y + 7) = 3(x + 8)$
Expand both sides: $4y + 28 = 3x + 24$

Step3: Rearrange to Ax+By=C form

Move all terms to one side to match the standard form, ensuring $A$ is positive.
$3x - 4y = 4$

Answer:

$3x - 4y = 4$