Question

question find the equation of a line perpendicular to $-5x + y = -2$ that passes through the point $(5, 4)$. answer $y = -\frac{1}{5}x + 5$ $-5x + y = -21$ $x - 5y = -15$ $y = \frac{1}{5}x + 5$

Explanation:

Step1: Find slope of given line

Rewrite $-5x + y = -2$ to slope-intercept form $y=mx+b$:
$y = 5x - 2$
Slope of given line $m_1 = 5$

Step2: Find perpendicular slope

Perpendicular slope $m_2 = -\frac{1}{m_1}$
$m_2 = -\frac{1}{5}$

Step3: Use point-slope form

Point-slope formula: $y - y_1 = m(x - x_1)$ with $(x_1,y_1)=(5,4)$
$y - 4 = -\frac{1}{5}(x - 5)$

Step4: Simplify to slope-intercept form

Expand and rearrange:
$y - 4 = -\frac{1}{5}x + 1$
$y = -\frac{1}{5}x + 5$

Step5: Verify other forms (optional)

Check if matches other options:
$y = -\frac{1}{5}x + 5$ can be rewritten as $x + 5y = 25$, which does not match the non-slope-intercept options.

Answer:

$y = -\frac{1}{5}x + 5$