Question

write the equation of the line which passes through the point (1, -2) and has a slope of $-\frac{2}{3}$.\
\bigcirc $2x + 3y = -4$\
\bigcirc $2x - 3y = -7$\
\bigcirc $2x + 3y = -1$\
\bigcirc $2x - 3y = 8$

Explanation:

Step1: Use point-slope form

$y - y_1 = m(x - x_1)$ where $(x_1,y_1)=(1,-2)$ and $m=-\frac{2}{3}$
$y - (-2) = -\frac{2}{3}(x - 1)$

Step2: Simplify the equation

$y + 2 = -\frac{2}{3}x + \frac{2}{3}$

Step3: Eliminate fractions

Multiply all terms by 3: $3y + 6 = -2x + 2$

Step4: Rearrange to standard form

$2x + 3y = 2 - 6$
$2x + 3y = -4$

Answer:

2x + 3y = -4