Question

question 5
find the equation of a line with given slope and containing the given point. write the equation in slope - intercept form.
$m = \frac{3}{2}$, point $(-6, -10)$
$y = $

Explanation:

Step1: Use point-slope form

The point-slope formula is $y - y_1 = m(x - x_1)$, where $m=\frac{3}{2}$, $x_1=-6$, $y_1=-10$. Substitute values:
$y - (-10) = \frac{3}{2}(x - (-6))$
Simplify to: $y + 10 = \frac{3}{2}(x + 6)$

Step2: Distribute the slope

Multiply $\frac{3}{2}$ across the parentheses:
$y + 10 = \frac{3}{2}x + \frac{3}{2} \times 6$
Calculate $\frac{3}{2} \times 6 = 9$, so:
$y + 10 = \frac{3}{2}x + 9$

Step3: Solve for y (slope-intercept)

Subtract 10 from both sides to isolate y:
$y = \frac{3}{2}x + 9 - 10$
Simplify the constants:
$y = \frac{3}{2}x - 1$

Answer:

$y = \frac{3}{2}x - 1$