Question

a line passes through the point $(-4, -3)$ and has a slope of $-dfrac{5}{4}$. write an equation in slope - intercept form for this line.

Explanation:

Step1: Use point-slope formula

The point-slope form is $y - y_1 = m(x - x_1)$, where $m=-\frac{5}{4}$, $x_1=-4$, $y_1=-3$.
$y - (-3) = -\frac{5}{4}(x - (-4))$

Step2: Simplify the equation

Simplify signs and distribute the slope:
$y + 3 = -\frac{5}{4}(x + 4)$
$y + 3 = -\frac{5}{4}x - 5$

Step3: Solve for y (slope-intercept)

Subtract 3 from both sides:
$y = -\frac{5}{4}x - 5 - 3$
$y = -\frac{5}{4}x - 8$

Answer:

$y = -\frac{5}{4}x - 8$