Question

write the slope - intercept equation of the function f whose graph satisfies the given conditions. the graph of f is perpendicular to the line whose equation is 5x - 7y - 14 = 0 and has the same y - intercept as this line. the equation of the function is (use integers or fractions for any numbers in the equation).

Explanation:

Step1: Rewrite given line to slope-intercept

First, rearrange $5x - 7y - 14 = 0$ into $y=mx+b$ form:
$-7y = -5x + 14$
$y = \frac{5}{7}x - 2$

Step2: Find perpendicular slope

Perpendicular slope is negative reciprocal:
$m_{\perp} = -\frac{7}{5}$

Step3: Identify shared y-intercept

From the rewritten line, $b = -2$

Step4: Write function equation

Substitute $m_{\perp}$ and $b$ into $y=mx+b$:
$y = -\frac{7}{5}x - 2$

Answer:

$y = -\frac{7}{5}x - 2$