Question

what is the equation of the line that passes through the point $(-2,-1)$ and has a slope of $\frac{5}{2}$?

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 $m=\frac{5}{2}$.
$y - (-1) = \frac{5}{2}(x - (-2))$

Step2: Simplify the equation

Simplify signs and expand the right side.
$y + 1 = \frac{5}{2}(x + 2)$
$y + 1 = \frac{5}{2}x + 5$

Step3: Isolate y to get slope-intercept form

Subtract 1 from both sides.
$y = \frac{5}{2}x + 5 - 1$
$y = \frac{5}{2}x + 4$
(To convert to standard form $Ax+By=C$:
Multiply all terms by 2: $2y = 5x + 8$
Rearrange: $5x - 2y = -8$)

Answer:

Slope-intercept form: $y = \frac{5}{2}x + 4$
Standard form: $5x - 2y = -8$