Question

what is an equation of the line that passes through the point (5, -1) and is perpendicular to the line 5x + 4y = 28?

Explanation:

Step1: Find slope of given line

Rewrite $5x + 4y = 28$ in slope-intercept form $y=mx+b$:
$4y = -5x + 28$
$y = -\frac{5}{4}x + 7$
Slope of given line: $m_1 = -\frac{5}{4}$

Step2: Find slope of perpendicular line

Perpendicular slopes are negative reciprocals:
$m_2 = \frac{4}{5}$

Step3: Use point-slope form

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

Step4: Simplify to slope-intercept form

$y + 1 = \frac{4}{5}x - 4$
$y = \frac{4}{5}x - 5$

Step5: Convert to standard form (optional)

Multiply by 5 to eliminate fractions:
$5y = 4x - 25$
$4x - 5y = 25$

Answer:

$y = \frac{4}{5}x - 5$ (or $4x - 5y = 25$)